Starting pitchers shouldn't be locked in if they are playing 2nd game of double header
I have David Price on my team. He was pitching 2nd game of double header vs. yankees. I noticed he was locked in before the start of the first game. It didn't matter this time, but a scenario could arise where the outcome of the early games decided if I wanted to start or bench him for the night game. Say after those games I was barely winning era, whip, bb, hrs. I would not want to jeopardize losing those categories then.
The lock is not by player, it is by team. So as soon as Price's team started the first game, all roster positions were locked for the day.