What works for me at the chin is I keep the skin as tight as possible and bring the razor straight down my chin and around my chin in one stroke which gets the upper, lower and undersides of my chin all at once. You need to quickly and continuously adjust the angle of the razor in this maneuver or you'll slice your chin. When I do my neck I come up against the grain right up to my chin and that gets what the last maneuver may have missed. Keeping the skin really pulled tight is really key in the neck areas.

I can't help you with the lip since I've had a moustache for the past 35 years now but if I had to I would use this neat 2/8s razor I have and probably do an arcing motion under my nose and down my lip and then use an off angle and come from the sides. But thats theory not practice.