I do the best I can as this area is prone to cuts if not careful. I shave with the grain on the first past with lots of buffing action and stick to across the grain for the other passes.
I suggest not shaving the lip but the skin above it.
On my second pass I go gently ATG (razorhead perpendicular to lip) and XTG (razorhead parallel to lip). I am not afraid of doing multiple strokes within one pass. With good lather, the slickness remains after the lather is gone, as long as I keep the razor a bit wet.