It's tradition Part 1

Actually, that's not true. A male lion welcomes its sons to stay without being exiled as long as they don't challenge their father for power (that's the condition most young male lions can't seem to get right). There was even a lion's pride on BBC that was MASSIVE (absorbing several prides into one) because it was led by a large, powerful male and his 4-5 large, fully-grown sons. Each of the sons had a small branch of the pride for their own on either side of the river and still answered to the father, and the father lion (when it couldn't defeat a lion on its own or with 1-2 of its sons) actually bellowed at the river's edge, and the rest of his sons came from across the shallow part of river to help battle. None of the other male lions stood a chance. In fact, in the instance I mentioned, the male actually ran off before the battle and abandoned the pride.

Goes to show, the obedient sons share in his father's bounty. The disobedient sons are cast out to fend for themselves. (That being said, some young male lions aren't exiled from their pride at all, but will actually leave themselves without any confrontation to find a place for themselves).

Turns out, animal social skills can be more advanced than people think.

So, as long as Simba doesn't challenge his father for power and acknowledges his father as king--he's good.