One could go old-school on the problem. Weld up a piece of iron
water pipe, such that one end is capped and there's a slot cut near
the top end to fit over the staple on the latch. The lock is placed
inside of the pipe and fastened through the staple as normal. If
done correctly, it's extremely difficult to get to the lock or latch
with anything but a key as the pipe restricts access to the lock as
well as the staple.
You landlord may not like that, however--but I've seen setups like
this all over the place here on timberland gates.
--Chuck