There could certainly be a genetic component, but there could be other factors at play too. Lack of hydration might be one; if you've had as bad a winter as many of us, the ewes may be a little shorter on milk than usual.
If it's minor, which it sounds as though it is, you might find that pinching the eyelid on the newborn lambs is as much as you need to do. Not very hard but just enough to make the eyelid puff slightly - stops it turning in again for a day or two, and things will hopefully have settled down by then.