Actually, removing the third eyelid does not even mean they have to be on drops for sure.

Our Cincy had cherry eye in one eye when she was 10 weeks old. That eyelid was reattached. A few weeks later, she had it in the other, and the vet opted to remove that eyelid. We were told to keep an eye on her, and watch for signs of dry eye, that she may have to go on drops, but she will be 6 next month and so far, no other issues, no drops needed.

Good luck with Reilly. Did the vet give you any medicine to put on his eye in the meantime?