Yeah I wouldnt panic if the bun is eating and pooping and acting ok, but I would get him/her to a vet. It sounds like it could just be conjunctivits or some sort of bacterial infection.
I would have a vet examine him/her to see if he needs antibiotics (orally or eye drops).
For now, tell your friend to get a warm wet cloth and gently wipe the eye off. Even holding the warm wet cloth against the eye will feel good to the bunny until he can get him/her to the vet.