Yes, you can feed them lettuce. It is good entertainment, keeps them active, and is a healthy & natural food. I disagree with the comments that recommend against it (which, I assume, are referring to iceberg lettuce).
Iceberg lettuce is a healthy food that will cause no negative effects. It has trace amount of beneficial nutrients. The statement that it has "no nutritional value" is a myth. It is low in calories. Actually, so low that it takes your body more calories to burn it than it provides (which is one important reason it is a healthy choice for most people). As far a nutrients (minerals/vitamins), in a 1-cup serving there is 102mg of potassium (good for heart and muscle function), and 13mg calcium, and small amounts of magnesium and iron. It also has 2 mg of vitamin C, a good amount of folate and some vitamin A and K. These, of course, are fairly minimal amounts---but even a LITTLE nutrients are still nutrients that are beneficial for your bird. As a steady diet it wouldn't be to their advantage. Several times a year I will throw them iceberg lettuce left over from family/school functions.