Mods tend to work the same on a LAN world as they do on a server because Minecraft treats any LAN host as a dedicated server. The "fatal error" is most likely being caused by a single mod not interacting properly. Please post crash logs and error messages so we the community can try to solve this problem.
https://www.minecraftforum.net/forums/mapping-and-modding-java-edition/minecraft-mods/mods-discussion/2572654-do-mods-not-work-over-lan-or
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