The reason why you see people talking about shooting .410 and .45 LC in the same gun is that they have the same base size - and a .410 shell can be safely fired in a .45 barrel without issue.
drew_235 is right, the .410 shotgun is nominally .410" barrel diameter - shooting a .45 LC in it might work - ONCE... with really negative results. Even if it was really a nominal .454" barrel, it'd be smoothbore and wouldn't stabilize the bullet either way.