For the dressing: in a small nonreactive bowl, whisk together the lime zest and juice, garlic, cumin, 3/4 teaspoon salt, and several grinds of black pepper. Whisk in the olive oil. Taste and season with more salt if needed. (Dressing can be prepared one day ahead. Cover and refrigerate. Bring to room temperature for 30 minutes and whisk well before using.)
For the salad: in a medium bowl toss the avocados, tomatoes, and red onion.
Pour half of the dressing over them and toss again gently. Reserve remaining dressing for tossing with the lettuce. Marinate the avocado mixture for at least 10 minutes or up to 30 minutes.
Iin a shallow salad bowl or in a large shallow serving dish, toss the romaine with just enough of the remaining dressing to coat it lightly. (You may have some left over.) Season the salad with salt and pepper. Spoon the avocado tomato mixture over the greens adding any juices collected in the bowl. Then sprinkle with queso fresco.
Note: Queso fresco is a mild, moist, snow-white Mexican cheese that crumbles easily.
It is sold in some grocery stores and Mexican markets. If unavailable, you can substitute feta.