i'm not too sure really, but the word "lettuce" rang alarm bells for me somewhat.. how much lettuce are you feeding him (and carrot too), because they only need the tiniest amounts of veg (actually they don't NEED any veg). I only give one tiny piece (half an inch square or less) less than every day and only of ONE veg or other. I never give lettuce because it's water content is too high and can give them diarrohea.
If you're feeding too much complementary food then he won't eat his mix (it's like giving a child a ton of cookies and wondering why they don't eat their dinner
)
They don't drink much and my dwarfs do drink about twice as much as Syrians. It could also be that he's getting so much water from the lettuce that he's not thirsty.
Unless he's underweight or looks too thin, don't feed him anything else other than his dry food for a while and see how that goes.
He also doesn't need to have chicken AND eggs in the same day. I'd just give chicken one day and egg a few days later. about 50% of days my hams don't have anything other than their dry food and when they do have a treat (e.g. chicken, egg, veg) they have one tiny piece of ONE of these only.