Preheat grill for medium heat and lightly oil the grate.
Thoroughly mix ground lamb, rosemary, thyme, garlic powder, salt, and pepper together in a bowl; shape into 4 patties.
Cook the burgers until they are beginning to firm and are hot and slightly pink in the center, about 5 minutes per side. An instant-read thermometer inserted into the center should read 140 degrees F (60 degrees C). Alternately, you can cook the burgers to your desired degree of doneness. Rest burgers while assembling toppings.
Mix mayonnaise and mustard together in a small bowl; spread 1 tablespoon of the mixture onto one side of each bun. Put a burger onto each bun and top with tomato and greens. Sandwich with remaining bun half to serve.