If you put a Mac in Lost Mode while FileVault is enabled, does it prevent OS X reinstalls? Apple's documentation on Lost Mode doesn't say a whole lot about what the finder of the Mac will be able to (or unable to) do with it. Especially if FileVault is enabled.

For example, if I lose my Mac while it is powered on with plenty of battery remaining, they'll see a lock screen and it probably won't connect to wifi unless they happen to be in a place with a known WiFi network (highly unlikely). That means the lock is unlikely to occur, and they're unlikely to ever see the lock message.

However, if they attempt an erase and restore, won't Disk Utility prevent them from erasing the volume since it'll be locked with the passwords of the accounts?

I suppose, theoretically, the only way for Lost Mode to actually do any good is if they figure out how to delete the volume in spite of the FileVault lock, install OS X, and then upon getting online have Apple lock it out during OS X activation?
Filevault prevents the theft of data not the device. If they boot to recovery partition or jump drive they can wipe and reinstall and your data is still safe. if you want to prevent that from happening you need to add a firmware password. So this would be the best combo 


filevault
firmware password
lost mode


however if they know what they are doing they can still open the machine and take it from there. 

There is no 100% fool proof way other keeping your mac with you