A new internal door is under $100 so don't go breaking any glass to get into that room...
I would either get a locksmith (someone said $165) but the risk is he can't open it, if so then/or...
... destroy that door latch by punching a bar through it and trying to turn the mechanism with some leverage such as a pipe wrench on the bar. Once that failed it would be a case if cutting the door set out with a skill saw or jig saw, opening the door, remove the door from the hinges and hang a new one.