Terms
Licence
Apache License 2.0, including an explicit patent grant. Commercial use, modification and redistribution are all permitted.
The toolkit itself
limn-toolkit depends on two libraries beyond the JDK, JSpecify's nullness annotations, which only a compiler reads, and a WebP decoder written in Java (org.glavo:webp), both Apache-2.0 too. The one other licence inside its jar is the Unicode License v3, which is permissive: what the toolkit knows about languages, such as which region a language means, which direction it runs in and which digits and plural forms it uses, is taken from the Unicode Consortium's CLDR, and the jar carries that licence beside it. The rendering backend adds LWJGL, which is BSD-3-Clause; the SVG renderer lunasvg with the plutovg it draws with, both MIT; and ANGLE, the OpenGL ES fallback for a Windows or macOS machine with no OpenGL driver, which is BSD-3-Clause and lists in each of its jars the sources compiled into it, with their licences. The native libraries LWJGL brings are permissive too, except OpenAL Soft, the audio output, which is LGPL-2.0-or-later: a shared library of its own, loaded at run time and replaceable.
Fonts and icons
Roboto, the default face, is Apache-2.0. The Noto fallback faces, for other scripts and for emoji, and the small symbol face that menus draw shortcut keys with, ship under the SIL Open Font License 1.1. The optional icon pack, limn-icons-tabler, is MIT. 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, used unmodified and kept as an isolated jar behind the audio decoder interface. Exclude that one dependency and you lose MP3 alone: an MP3 is then refused as a format the backend does not read, and WAV and Ogg Vorbis keep working. That removes one LGPL component, not every one: the backend still carries OpenAL Soft, the LGPL audio output above.
FFmpeg video, and what ships with it
The optional video decoder, for H.264, HEVC, VP9 and VP8 in MP4 and Matroska, links a trimmed FFmpeg dynamically, built as LGPL-2.1-or-later. Its native libraries are an artifact of their own, limn-ffmpeg-natives, one classifier per desktop target, and limn-video-ffmpeg-natives-all names all of them for a bundle that ships everywhere, so a distribution that includes limn-video-ffmpeg and those libraries is distributing FFmpeg, and each of those jars carries the licence text and the notice that requires. They are dynamically linked and replaceable, which is what that licence asks. None of Limn's other libraries 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.