In Florida, lettuce is a cool season crop which is typically sown at the beginning or end of winter. It likes temperatures between 50-70 degrees F. and February is a good time to get seeds going. As temps warm up in Spring, you may still get a crop, but would be better off trying fast maturing lettuces, such as mesclun or baby lettuce. They tolerate shade well, so you might even be able to stretch the season a little by giving them shade as it warms up. You can read all about growing vegetables in Florida, including lettuce and suggested varieties for our area at the IFAS guide for Florida Vegetable Gardening. Another good publication can be found here: Winter salad.
Pictured below is an awesome ‘salad bowl’, which is a portable container garden, giving you both flexibility and food. Check it out!