I just noticed my battery is out of place and the lock latch is stuck, I can't remove the battery. I tried to unscrew the entire laptop but couldn't get the laptop apart, hoping I could wiggle the battery or latch some how. Any ideas?
Since it is a Lenovo ThinkPad T240 unit, I would suggest just contacting their technical support, explaining that the battery is stuck, and ask them how to "un-stick" it so that the battery can be removed. I cannot say I have heard of this problem before, but chances are, one of their techs has, can can walk you through fixing things.
I know this is going to sound obvious, but since you haven't mentioned it specifically I may as well ask: have you pushed the battery back in to place before trying to pull on the latch? Looking at that picture it looks like the battery isn't lined up properly which may be why the latch is stuck.
I assume you mean that that latch won't move in either direction at all? Just to state the obvious just in case it may help, you do have to actually hold that switch to the unlocked position to remove the battery on that laptop. I'm on a similar model right now and you can flip it between lock and the middle, but middle still doesn't release unless you actively hold it to the unlock position.
Push the battery back into its original position to the best of your ability and try to force the latch open or closed. If the battery is swollen(bad) then i'd go with trying your best to force it back into position to open the latch and remove it, worst case try to force it out.