Rental? Get the landlord to fix it properly.
If it's your place and it's just a handle you grab, I would look at moving it up or down slightly and drilling new holes with some proper metal screws.
TBH it really looks like the whole thing is past it's use by date. Where has the lock mechanism gone?
Yeah it is old, and for some reason the whole door was put in back to front, so what you would normally consider as the outside door, is actually on the interior and vice versa.... but this whole house is like that. Love wanna-be builders from the early 80's....... :D