I haven't had a LTA, but my BTA and mag have behaved this way when unhappy because of oxygen levels, nitrates, bacteria, or lighting being out of whack.
I've never seen my BTA's split (I usually find the bundle of joy out sunny himself and know that it happened after the fact), but I've heard they will go under a rock to split.
I'd take a critical look at your tank and try to figure out why he isn't happy.