Crumble cotija cheese and put in a bowl. Place crema and salsa in containers. Rinse lettuce, cilantro, and green onions. Finely shred enough lettuce to make about 5 cups and place in a container. Chop cilantro and thinly slice onions (including green tops); put in containers. Pit and peel avocados, thinly slice into a bowl, and mix with 2 tablespoons lime juice.
In a 2- to 3-quart covered pan over medium heat, stir beans often until hot (adding a little water, if needed, to refried beans), about 5 minutes. Transfer to a bowl and keep warm. Or heat, covered, in a microwave oven at full power (100%), stirring once, until hot, 3 to 4 minutes. If using whole beans, lift beans from liquid with a slotted spoon or drain in a colander.
Tear cooked meat into coarse shreds or cut into thin slices. If using a whole roast chicken, pull meat off bones and shred; sliver skin and include (or discard if desired). If meat is raw, grill it, then slice into bite-size pieces. Serve warm or at room temperature. To reheat, place meat in a microwave-safe bowl, cover, and heat in microwave oven at half power (50%), stirring occasionally, 2 to 3 minutes.
Drizzle 1/4 cup water over a dish towel. Wrap tortillas in towel and overwrap with microwave-safe plastic wrap. Heat in a microwave oven at full power (100%) until hot and steamy, 1 to 2 minutes. Remove plastic wrap and set towel-wrapped tortillas in a basket or covered casserole.
Arrange cheese, crema, salsa, lettuce, cilantro, onions, avocados, beans, meat, and tortillas on the table.
Note: Nutritional analysis is per burrito with chicken.