LC I: No. The LC I required a new case for any upgrade to a later model. Use the base of a discarded II/III/III+/475 and swap the floppy drive bracket with one from an LCIII if you want to try it, but due to the difference in components in this model, you're best letting it be and upgrading another machine.
LC II: Yes. Every component inside the computer except the RAM is swappable to the new logic board.
LC III: Again, yes, and this time the RAM can transfer to the new board.
LC III+: See above.
Don't forget you need 7.1 or later for an LC475. Make sure you're using Enabler 065 if you go with 7.1 (7.5 and later versions don't need enablers).