Much like Celery and Celery Root, you can eat both the Celtuce Leaves and Celtuce Stem. Celtuce's favorite meals are stir fries such as Stir-Fried Celtuce Stem and Tofu & Lettuce Stem Stir Fry with Pan Fried Noodles. You can even enjoy Celtuce Stem raw as Celtuce Noodle Salad.
P.S. If you are looking for Celtuce at the market, be on the lookout for his various aliases, including: stem lettuce, celery lettuce, asparagus lettuce, Chinese lettuce, wosun, and woju.