Ken,
I was glad to read your post because I was going to make the exact same one. I finished radiation 7 months ago and the weather has turned very cold in New England and with it, my lips have been incredibly dry.
I usually put Aquaphor on them 5-6 times a day and it is a big help. I carry around a small tube of Aquaphor so I have it at hand all the time. The best size isthe free sample size that I got while getting radiated.
Lip balms don't cut it. I've tried Vaseline which works pretty well too. Someone recommended taking apart a Vitamin E capsule and spreading the liquid on my lips but I've not yet tried that. Trouble with Aquaphor is that you leave lip prints on everything!

- Sheldon