I would recommend a full breakdown at the end of the shooting season and the gun is going to be put away for a couple of months.
You will need a mainspring clamp to take the lock apart and properly fitting screwdrivers. The full takedown of a lock depends on how much the rifle has been shot and how dirty the interior of the lock is. For the most part, a good cleaning can be done by a tooth brush and warm water with maybe a bit of soap. Dry with a clean cloth and spray the internals with Barricade for storage. If the lock is heavily fouled and feels sluggish, then it needs to be taken apart. Do this in a box with a white cloth or layer of white paper towels to keep the parts visible. As the lock is taken apart lay the parts down in an organized fashion in relation to where the parts came from. Pay special attention to the fly. On an L&R lock, the fly can be replaced two ways. Lay it on the surface as it is removed from the tumbler. Once the lock is taken apart, each piece can be cleaned separately. When reassembling the lock, I use a rust inhibiting grease sparingly on the threads and the rubbing surfaces and very sparingly in the fly recess in the tumbler. Tighten screws to a snug fit since parts also need to move such as the tumbler and the seer. Once assembled, cycle the lock by hand to verify smooth action with no drag.