LambDynamicLights v2.3.1 seems not compatible for Minecraft 1.20 if I check for updates that should work normally like all others mods.
I started the client and the mod seems to works fine after installing the required Fabric API beta version.

If I'm not wrong when I installed the mod from the Launcher it says like something about meta data or something.

Update to Minecraft 1.20.1 as it's a very minor release most mods should work.