Terms
Licence
Apache License 2.0, including an explicit patent grant. Commercial use, modification and redistribution are all permitted.
The toolkit itself
limn-toolkit has no dependencies beyond the JDK, so for it Apache-2.0 is the whole story. The rendering backend adds LWJGL, which is BSD-3-Clause.
Fonts
Roboto and the Noto fallback faces ship under the SIL Open Font License. Every bundled component is listed with its licence in the project's NOTICE file.
MP3 decoding is LGPL
MP3 support comes from JLayer, which is LGPL-2.1 and is kept as an isolated jar behind the audio decoder interface. Exclude that one dependency if your distribution needs to avoid LGPL obligations; WAV and Ogg Vorbis keep working.
FFmpeg video, and what ships with it
The optional H.264 decoder links a trimmed FFmpeg dynamically, built as LGPL-2.1-or-later. Its native libraries ride in one classifier per desktop target, and in natives-all for a bundle that ships everywhere, so a distribution that includes limn-video-ffmpeg is distributing FFmpeg, and the jar carries the licence text and the notice that requires. They are dynamically linked and replaceable, which is what that licence asks. Nothing else depends on this module: leave it out and every other media format keeps working.
None of this is legal advice. Read the licences, and ask your own counsel.