If it is an aquatic turtle (lives in a tank that's mostly/all water) it is most likely omnivorous and should enjoy earthworms, softshelled insects, raw liver (not frequently though), tomatoes, apples, banana (as a treat), strawberries, live feeder fish (comets, guppies, minnows--cheap at most pet stores), and most pellets for aquatic turtles (I recommend those, as their specially formulated to help maintain a healthy and balanced diet). If it is a box turtle (has a hinge on the
bottom of it's shell, allowing it to "box" itself inside it's shell) it can live on the same basic diet, but with the majority of it's diet being vegetables. They make specially formulated pellets for box turtles as well, but I prefer to stick to fresh fruits and vegetables (sometimes mealworms--she loves chasing 'em around the food dish), because the pellets can get messy, although they are good for them. If it is terrestrial (a tortoise--lives completely on land, usually doesn't have hinges) they can live on the same basic diet, but eliminate ALL animal matter from the diet, and steer clear of foods with large amounts of protein. He/she should also get (if they haven't already) a UV lamp--one specificly for reptiles-- a heat lamp, and if it's aquatic a basking platform for it to get out of the water and dry off to prevent fungus. You may want to use a calcium supplement as well, as turtles often have a hard time getting the calcium they need while in captivity. If it is aquatic, you should have at least 10 gallons of water per inch of shell, so eventually--really soon, actually--he'll have to invest in a large tank. It can be very helpful, for future references, to buy a book about the kind of turtle it is--or at least one about aquatic turtles (or terrestrial if it's a box turtle or tortoise--you can check with someone at the pet store to see what kind it is; bring a picture, it could be extremely helpful). That's about as much as I can help without knowing exactly what kind of turtle it is. hope I helped! : )
ps. Lettuce and carrots are ok, but turtles need more variety in their diet. And try to avoid iceburg lettuce--it has very little nutritional value for turtles; it's just empty calories.
Personal experience--I own 2 red eared sliders and an eastern box turtle.