There's a few edge cases that you'd probably need to handle (like adding the same word with two different definitions), but probably few enough that you could do them ad-hoc and punt to the user. ("Hey, merging these two sets failed, here's the conflict, which do you want to keep?")

Something fancy like Operational Transforms or CRDT might make your life easier if you find a library that's ergonomic for your use case, but it's definitely not necessary.