Most common oils are adequate for locks, but they're most effective when the locks are clean and dry.. when new.
Applying some oil into the key passageway (padlock turned upside-down) and also applied to the locking and other shackle hole, will leave a coating of oil on all of the internal parts. Working the lock from locked/open numerous cycles will distribute the oil over the surfaces of the moving parts. With the parts oiled, water won't stick to the moving parts. Some of the oil will at least partially fill cavities that could trap water, preventing water from accumulating where it would cause problems. Oiled parts are less likely to be completely fouled by superglue vandals.
Padlocks that have been outdoors with no protection will generally be problematic eventually. Those locks would benefit from being flushed with solvent, blown out with compressed air, dried, then lubricated with oil. If excess oil comes out dark with dirt, repeat the flushing, etc.
For the best results, as suggested already, put a shield in place to deflect water and dirt, and prevent it from entering the lock. One of the cheapest and most effective shields I've seen, has been a rubber flap cut from an inner tube.
Mowing and trimming often kick up a lot of dirt, and it's likely that some of that dirt can find it's way into unprotected padlocks. The fine dirt particles will cause wear of the internal parts.. then the lock gets fiddly, and eventually it won't unlock.
Antique locks generally worked fine without lubricants, which I attribute to better choices of metals, better designs and more precise part manufacturing. More recent locks are generally made as cheaply as possible with rapidly produced parts, which aren't reflective of a precision, high reliability mechanism.
One of the PB Blaster penetrating oil products contains teflon, which I've found to be useful in lubricating locks and door latches/mechanisms/hardware.. it needs to be shaken well to suspend the teflon into the solvent. I've replaced the spray nozzle with a spray head that accepts an extension tube. This has been very effective at lubricating commercial entry/exit doors, exposed to the outdoor elements, and difficult to access locks/latches, without removing the locking mechanisms from the doors.