In a small bowl, combine the couscous and 1/4 cup hot tap water. Let sit for 5 minutes; fluff with a fork.
In a food processor, puree the egg, sunflower seeds, and 3/4 cup of the lentils until they form a paste; transfer to a bowl. Mix in the carrot, onion, lemon juice, couscous, the remaining lentils, 1/2 teaspoon salt,and 1/4 teaspoon pepper. Form the mixture into four 1/2-inch-thick patties. Refrigerate, uncovered, until firm, 20 to 25 minutes.
Heat grill to medium-high. Oil the grill grate. Grill the patties, turning once (do not press or flatten), until charred and heated through, 4 to 5 minutes per side. Serve on rolls with the desired toppings.