Mine get vegetables daily, but on a rotation. So they're getting a different mix of 3-5 vegetables each day (Alongside a rotation of proteins, carbs, etc, and a staple of their usual lab block. Fruit is given occasionally as I see fit). I also keep a dated logbook of what they get every time I replace the food or give them a treat so that I can track detailed nutritional information. I give approx. 1Tbsp of fresh vegetable mix per mouse, though they never finish it and I could probably cut it back without them caring.
Fruit is very high in sugar, and should be given less often than vegetables. You'll probably get mixed answers from different people. It can be really hard to get solid information on certain small mammals!
I see nothing wrong with giving (varied) vegetables daily, other people will probably tell you it should only be a rare treat. Keep an eye out for loose stool and other signs of an unhealthy animal, and make your own adjustments. Of course, moderation is key, and consider limiting it
hard if they refuse their primary diet in favor of only their vegetables. My ladies actually don't especially like fruit, and only eat a small portion of the vegetables I give them each day, they really prefer their lab block and live bugs.
I log the nutrition of what I've been feeding at the end of each week, and if need be, make adjustments to my feeding the next week, basing my guidelines primarily on a mixture of the following sources:
https://www.nap.edu/read/4758/chapter/5#85
http://www.afrma.org/bc_mineralproteinmice.htm
http://www.allaboutmice.co.uk/nutrition/
(Note: I am not recommending everyone become as...Neurotic, as I am, I'm just sharing my own experiences and what I do in my own feeding)
On Lettuce:
I wouldn't feed it myself, Mice only eat so much in a day and Romain Lettuce is rather nutritionally thin.
While it contains 148% of a human's daily Vit.A, it lacks in most other departments.
Much better than iceburg lettuce I suppose, which is just crunchy water, really.