I took a very small piece of duct tape and rolled it into a small tube shape, bent that into a U shape, trimmed, and wrapped it around under the gas button of a mini-Bic. Held it in place with another small piece of duct tape circling the head of the lighter. The zip-tie others have suggested sounds better, except that would leave a bump at the locking part of the zip-tie which seems like it would snag on things. Then I used ranger bands (cut up bicycle inner tube) to attach the lighter to a P-51 can opener. The hole in the P-51 attaches to my keyring with a small split ring. The lighter pins the hook part of the P-51 safely between the lighter body and the back of the P-51. The head of the lighter and the hook end of the P-51 are on the end away from the keyring.

The cases I have seen for lighters that attach to your keyring all doubled or tripled the size of the lighter, which was not what I wanted. So far my homemade setup has worked perfectly, but I'll admit it looks a bit funky!