Lunar and Labymod may be breaking the lgpl license of sodium by embedding it inside their own closed source jars

Lunar Client does comply with the license to the extent legally necessary. The source code can be found here, and here, with instructions on how to find these open-source licences in the launcher. labymod does have a github, but I couldn't find anything on their bundling of FOSS anywhere.

LGPL explicitly allows linking with closed source code - that's the difference between it and GPL