If another player gains control of the chosen creature while Tyrannical Pitlord is still on the battlefield, that creature will continue to have flying and get +3/+3.

If the chosen creature leaves the battlefield, you can’t choose a new creature.

If Tyrannical Pitlord enters the battlefield at the same time as another creature, that creature can’t be chosen.

The ability of Tyrannical Pitlord that allows you to choose a creature isn’t a triggered ability and doesn’t use the stack. Players can’t respond to your choice of which creature it’s affecting.

If Tyrannical Pitlord’s leaves-the-battlefield triggered ability resolves while its controller is not the same as the controller of the chosen creature, that creature will not be sacrificed.