Sounds like that's probably the right door lock for your trailer. Congratulations on your find!
Do you have a key for it? Vintage Trailer Supply does
have replacement cylinders with keys for this model lock.
L-77 L-66 Lock Cylinder
On the other hand, we never locked our Pacer as the cylinder was kind of cranky and we didn't want to get locked out. In addition to which, we figured anything anybody would steal out of the trailer would cost less than repairing the lock and door if anybody broke in. (And nothing ever got stolen.)