I haven't had a dog with this condition but I'm an eye doctor & sees lots of folks with it. It's called entropion & the runny eye is from the irritation caused by the lashes rubbing against the eye. If it continues, it can lead to permanent damaged to the cornea (the clear outer covering), corneal ulcers and/or chronic conjunctivitis.
Surgery is a last option after other measures are tried. The lid muscle goes into spasm & causes the lid to turn in. That lid muscle can be stretched & the entropion can be reversed. Whenever you can, pull the lid down (or up , whichever lid is the problem) by putting your finger about 1/2 inch away from the eye & gently sliding the lid away from the eye - you'll see the lid turn back out where it belongs - wait 3-5 seconds & then gently release. Repeat 5 times, at least 4 times a day. Do this as often as possilble -even when there is no turning in of the lid - so that muscle learns to stay loose. It doesn't hurt your pup to do this muscle stretching & you can make it a routine part of your snuggle time so the pup won't even notice you doing it.
A warm compress helps to relax the muscle, in conjunction with the lid stretches, but I'm not sure your pup will want to hold still for a warm, wet wascloth held over the eye for 5 minutes, 4 times a day - but you can give it a try. I also sometimes have my patients put tape on the skin under their eye & attach it onto their cheek to help keep the lid in the stretch position for 5-10 minutes, but, your pup might not like the tape on his face.
Your pup might also outgrow this condition but in the meantime keep a careful eye on his cornea for signs of potential problems - goopy discharge, debris, cloudiness or his rubbing his eye with his paws or against the carpet.
Good luck - keep us posted.