Is it possible for ocular herpes to spread to another person's lips?

Contact. Only if one kisses the eye when the lesions are fresh and open. It can move in the other direction also. This would be rare, not common. More often one with a fresh herpes lesion rubs their eye, then touches something that the person with the vulnerable lips also touches and then rubs the lips.
Yes. The herpes virus type one lives in the trigeminal ganglion of the brain. It can travel to the lips, nose or eye and is contagious to those persons who have not been exposed to the virus before and thus have no antibodies.