LanguageTool is published under the GNU Lesser General Public License (LGPL).
For more detailed license information, see COPYING.txt and README.md.

This is the list of libraries used by LanguageTool and their licenses:

at.favre.lib:bcrypt:0.6.0 - Apache License, Version 2.0
at.favre.lib:bytes:0.8.0 - Apache License, Version 2.0
ch.qos.logback:logback-classic:1.2.3 - Eclipse Public License - v 1.0 & GNU Lesser General Public License
ch.qos.logback:logback-core:1.2.3 - Eclipse Public License - v 1.0 & GNU Lesser General Public License
com.auth0:java-jwt:3.12.0 - The MIT License (MIT)
com.beust:jcommander:1.78 - Apache License, Version 2.0
com.carrotsearch:hppc:0.8.2 - Apache License, Version 2.0
com.fasterxml.jackson.core:jackson-annotations:2.12.0 - The Apache Software License, Version 2.0
com.fasterxml.jackson.core:jackson-core:2.12.0 - The Apache Software License, Version 2.0
com.fasterxml.jackson.core:jackson-databind:2.12.0 - The Apache Software License, Version 2.0
com.github.lucene-gosen:lucene-gosen:6.2.1 - The Apache License, Version 2.0
com.gitlab.dumonts:hunspell:1.1.1 - Apache License 2.0
com.google.android:annotations:4.1.1.4 - Apache 2.0
com.google.android.tools:dx:1.7 - Apache 2.0
com.google.api.grpc:proto-google-common-protos:2.0.1 - Apache-2.0
com.google.code:cjftransform:1.0.1 - Apache License 2.0
com.google.code.findbugs:jsr305:3.0.2 - The Apache Software License, Version 2.0
com.google.code.gson:gson:2.8.6 - Apache 2.0
com.google.errorprone:error_prone_annotations:2.3.4 - Apache 2.0
com.google.guava:failureaccess:1.0.1 - The Apache Software License, Version 2.0
com.google.guava:guava:30.1-jre - Apache License, Version 2.0
com.google.guava:listenablefuture:9999.0-empty-to-avoid-conflict-with-guava	The Apache Software License, Version 2.0
com.google.j2objc:j2objc-annotations:1.3 - The Apache Software License, Version 2.0
com.google.protobuf:protobuf-java:3.17.2 - 3-Clause BSD License
com.hankcs:aho-corasick-double-array-trie:1.2.2 - Apache License Version 2.0
com.hankcs:hanlp:portable-1.7.8 - Apache License Version 2.0
com.ibm.icu:icu4j:56.1 - ICU License
com.intellij:annotations:12.0 - Apache License 2
com.nativelibs4java:bridj:0.7.0 - New BSD License (GPL-compatible)
com.optimaize.languagedetector:language-detector:0.6 - Apache 2
com.sparkjava:spark-core:2.9.3 - The Apache Software License, Version 2.0
com.sun.istack:istack-commons-runtime:3.0.5 - CDDL 1.1 & GPL2 w/ CPE
com.sun.xml.fastinfoset:FastInfoset:1.2.13 - Apache License, Version 2.0
com.vdurmont:emoji-java:5.1.1 - The MIT License
commons-beanutils:commons-beanutils:1.9.4 - Apache License, Version 2.0
commons-cli:commons-cli:1.4 - Apache License, Version 2.0
commons-codec:commons-codec:1.14 - Apache License, Version 2.0
commons-digester:commons-digester:2.1 - The Apache Software License, Version 2.0
commons-io:commons-io:2.8.0 - Apache License, Version 2.0
commons-logging:commons-logging:1.2 - The Apache Software License, Version 2.0
commons-validator:commons-validator:1.7 - Apache License, Version 2.0
de.danielnaber:german-pos-dict:1.2.2 - Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
de.danielnaber:jwordsplitter:4.5 - The Apache Software License, Version 2.0
edu.washington.cs.knowitall:opennlp-chunk-models:1.5 - The Apache Software License, Version 2.0
edu.washington.cs.knowitall:opennlp-postag-models:1.5 - The Apache Software License, Version 2.0
edu.washington.cs.knowitall:opennlp-tokenize-models:1.5 - The Apache Software License, Version 2.0
edu.washington.cs.knowitall:openregex:1.1.1 - LGPL (GNU Lesser General Public License)
io.github.jimregan:languagetool-ga-dicts:0.02 - GNU General Public License, Version 2.0
io.github.resilience4j:resilience4j-circuitbreaker:1.7.1 - Apache-2.0
io.github.resilience4j:resilience4j-core:1.7.1 - Apache-2.0
io.github.resilience4j:resilience4j-micrometer:1.7.1 - Apache-2.0
io.grpc:grpc-api:1.42.1 - Apache 2.0
io.grpc:grpc-context:1.42.1 - Apache 2.0
io.grpc:grpc-core:1.42.1 - Apache 2.0
io.grpc:grpc-netty-shaded:1.42.1 - Apache 2.0
io.grpc:grpc-protobuf:1.42.1 - Apache 2.0
io.grpc:grpc-protobuf-lite:1.42.1 - Apache 2.0
io.grpc:grpc-stub:1.42.1 - Apache 2.0
io.lettuce:lettuce-core:6.1.5.RELEASE - Apache License, Version 2.0
io.micrometer:micrometer-core:1.7.1 - The Apache Software License, Version 2.0
io.micrometer:micrometer-registry-prometheus:1.7.1 - The Apache Software License, Version 2.0
io.netty:netty-buffer:4.1.68.Final - Apache License, Version 2.0
io.netty:netty-codec:4.1.68.Final - Apache License, Version 2.0
io.netty:netty-common:4.1.68.Final - Apache License, Version 2.0
io.netty:netty-handler:4.1.68.Final - Apache License, Version 2.0
io.netty:netty-resolver:4.1.68.Final - Apache License, Version 2.0
io.netty:netty-transport:4.1.68.Final - Apache License, Version 2.0
io.perfmark:perfmark-api:0.23.0 - Apache 2.0
io.projectreactor:reactor-core:3.3.20.RELEASE - Apache License, Version 2.0
io.prometheus:simpleclient:0.12.0 - The Apache Software License, Version 2.0
io.prometheus:simpleclient_common:0.10.0 - The Apache Software License, Version 2.0
io.prometheus:simpleclient_guava:0.12.0 - The Apache Software License, Version 2.0
io.prometheus:simpleclient_hotspot:0.12.0 - The Apache Software License, Version 2.0
io.prometheus:simpleclient_httpserver:0.12.0 - The Apache Software License, Version 2.0
io.prometheus:simpleclient_tracer_common:0.12.0 - The Apache Software License, Version 2.0
io.prometheus:simpleclient_tracer_otel:0.12.0 - The Apache Software License, Version 2.0
io.prometheus:simpleclient_tracer_otel_agent:0.12.0 - The Apache Software License, Version 2.0
io.vavr:vavr:0.10.2 - The Apache Software License, Version 2.0
io.vavr:vavr-match:0.10.2 - The Apache Software License, Version 2.0
javax.activation:javax.activation-api:1.2.0 - CDDL/GPLv2+CE
javax.annotation:javax.annotation-api:1.3.2 - CDDL + GPLv2 with classpath exception
javax.measure:unit-api:1.0 - BSD
javax.servlet:javax.servlet-api:3.1.0 - CDDL + GPLv2 with classpath exception
javax.xml.bind:jaxb-api:2.3.0 - CDDL 1.1 & GPL2 w/ CPE
junit:junit:4.13.2 - Eclipse Public License 1.0
net.arnx:jsonic:1.2.11 - The Apache Software License, Version 2.0
net.loomchild:segment:2.0.1 - MIT License
org.apache.commons:commons-collections4:4.1 - Apache License, Version 2.0
org.apache.commons:commons-lang3:3.11 - Apache License, Version 2.0
org.apache.commons:commons-pool2:2.9.0 - Apache License, Version 2.0
org.apache.commons:commons-text:1.9 - Apache License, Version 2.0
org.apache.lucene:lucene-backward-codecs:5.5.5 - Apache 2
org.apache.lucene:lucene-core:5.5.5 - Apache 2
org.apache.opennlp:opennlp-tools:1.9.4 - Apache License, Version 2.0
org.carrot2:morfologik-fsa:2.1.7 - BSD
org.carrot2:morfologik-fsa-builders:2.1.7 - BSD
org.carrot2:morfologik-speller:2.1.7 - BSD
org.carrot2:morfologik-stemming:2.1.7 - BSD
org.carrot2:morfologik-tools:2.1.7 - BSD
org.checkerframework:checker-qual:3.5.0 - The MIT License
org.eclipse.jetty:jetty-client:9.4.44.v20210927 - Apache Software License - Version 2.0 & Eclipse Public License - Version 1.0
org.eclipse.jetty:jetty-http:9.4.44.v20210927 - Apache Software License - Version 2.0 & Eclipse Public License - Version 1.0
org.eclipse.jetty:jetty-io:9.4.44.v20210927 - Apache Software License - Version 2.0 & Eclipse Public License - Version 1.0
org.eclipse.jetty:jetty-security:9.4.44.v20210927 - Apache - Software License - Version 2.0 & Eclipse Public License - Version 1.0
org.eclipse.jetty:jetty-server:9.4.44.v20210927 - Apache Software License - Version 2.0 & Eclipse Public License - Version 1.0
org.eclipse.jetty:jetty-servlet:9.4.44.v20210927 - Apache Software License - Version 2.0 & Eclipse Public License - Version 1.0
org.eclipse.jetty:jetty-util:9.4.44.v20210927 - Apache Software License - Version 2.0 & Eclipse Public License - Version 1.0
org.eclipse.jetty:jetty-util-ajax:9.4.44.v20210927 - Apache Software License - Version 2.0 & Eclipse Public License - Version 1.0
org.eclipse.jetty:jetty-webapp:9.4.44.v20210927 - Apache Software License - Version 2.0 & Eclipse Public License - Version 1.0
org.eclipse.jetty:jetty-xml:9.4.44.v20210927 - Apache Software License - Version 2.0 & Eclipse Public License - Version 1.0
org.eclipse.jetty.websocket:websocket-api:9.4.44.v20210927 - Apache Software License - Version 2.0 & Eclipse Public License - Version 1.0
org.eclipse.jetty.websocket:websocket-client:9.4.44.v20210927 - Apache Software License - Version 2.0 & Eclipse Public License - Version 1.0
org.eclipse.jetty.websocket:websocket-common:9.4.44.v20210927 - Apache Software License - Version 2.0 & Eclipse Public License - Version 1.0
org.eclipse.jetty.websocket:websocket-server:9.4.44.v20210927 - Apache Software License - Version 2.0 & Eclipse Public License - Version 1.0
org.eclipse.jetty.websocket:websocket-servlet:9.4.44.v20210927 - Apache Software License - Version 2.0 & Eclipse Public License - Version 1.0
org.glassfish.jaxb:jaxb-core:2.3.0 - CDDL+GPL License
org.glassfish.jaxb:jaxb-runtime:2.3.0 - CDDL+GPL License
org.glassfish.jaxb:txw2:2.3.0 - CDDL+GPL License
org.hamcrest:hamcrest-core:1.3 - New BSD License
org.hdrhistogram:HdrHistogram:2.1.12 - BSD-2-Clause & Public Domain, per Creative Commons CC0
org.ioperm:morphology-el:1.0.0 - Apache License, Version 2.0 & Creative Commons Attribution-ShareAlike 4.0 International License
org.jetbrains:annotations:20.1.0 - The Apache Software License, Version 2.0
org.jetbrains.intellij.deps:trove4j:1.0.20200330 - GNU LESSER GENERAL PUBLIC LICENSE 2.1
org.json:json:20170516 - The JSON License
org.jvnet.staxex:stax-ex:1.7.8 - Dual license consisting of the CDDL v1.1 and GPL v2
org.latencyutils:LatencyUtils:2.0.3 - Public Domain, per Creative Commons CC0
org.mariadb.jdbc:mariadb-java-client:2.7.4 - LGPL-2.1
org.mybatis:mybatis:3.5.6 - The Apache Software License, Version 2.0
org.reactivestreams:reactive-streams:1.0.3 - CC0
org.slf4j:slf4j-api:1.7.30 - MIT License
org.softcatala:catalan-pos-dict:2.16 - GNU General Public License, Version 2, June 1991 & GNU Lesser General Public License, Version 2.1, February 1999
org.softcatala:spanish-pos-dict:1.4 - GNU Lesser General Public License, Version 2.1, February 1999
tech.units:indriya:1.3 - BSD
tech.uom.lib:uom-lib-common:1.1 - BSD
ua.net.nlp:morfologik-ukrainian-lt:5.6.0 - GNU Lesser General Public License

Other resources like dictionaries are not technically libraries, they may have 
different licenses (including GPL) without affecting LanguageTool's licensing. 
For the dictionaries that are used for spell checking, see
./org/languagetool/resource/<xx>/hunspell/README*
and
./org/languagetool/resource/<xx>/spelling/README* (<xx> = language code).