So I just beat the Automatron DLC and I go up the elevator to leave and as I'm leaving the mechanist's lair during the load screen my game crashes for no reason, I reset the game and try again and it was the same thing. Basically I can't leave the mechanist's lair without crashing. Help?

You could try walking out the way you came in, though the Robco Office, as opposed to using the "Garage" exit.
Other option would be to "fast travel" out seeing as this particular cell is an interior type of limited settlement.
Fast travel works from the Mechanist's Lair once completed.

Please post your issue in the http://www.gamesas.com/forum/334-fallout-4-automatron-dlc-support/ section.