Grilled Lamb Burgers with Red Onion Aïoli

Name: Grilled Lamb Burgers with Red Onion Aïoli
Ingredients: 1 1⁄2 lb. ground lamb; 1 1⁄2 tsp. ground cumin; Kosher salt and freshly ground black pepper, to taste; 5 cloves garlic, peeled and wrapped in aluminum foil; 1 large red onion, sliced crosswise into ¼”-thick rings; 1 cup olive oil; 2 egg yolks; Juice and zest of 1 lemon; 1⁄2 cup canola oil; 2 medium ripe Hass avocados; Juice of 1 lime; 4 hamburger buns, split; Thinly sliced romaine lettuce and tomatoes, for serving; 4 fried eggs, for serving