Too much of a good thing. You only need a light film, mainly to prevent water from wicking into the crevices. Since you have chain oil and WD-40, open the the lock and put a drop or two of the chain oil on the steel sliding latch, and then spray on WD-40 to carry it in and spread it around. Then spray WD-40 into the key area. Dry off any excess and overspray and let the lock dry overnight.

You'll need to do this every once in a while in the winter, but probably only once in the summer if that. Use the locks feel as your indicator that it needs a repeat treatment.