Interesting.
I have noticed that the first pick is sweet, then bitterness slowly increases over 10-11 weeks from the first pick, in spring and summer, my main seasons for growing lettuce.
I think that the closer a lettuce is to flowering, the more bitter its leaves. But in moist compost and favourable weather, leaves are sweeter. In full sunlight as I hardly ever grew lettuce in much shade.
So your experience slightly contradicts that and like so many things, its multi faceted.
I would try out some different varieties for one thing and grow lots of other ingredients too like pea shoots, spinach and sorrel, but I expect you are already doing that.
Good luck with the restaurant.
