Heat olive oil in a large frying pan over medium-low heat; cook and stir garlic and sugar in the hot oil until garlic is lightly browned, 3 to 5 minutes. Mix leeks into garlic mixture; cook and stir until leeks are lightly browned, about 10 minutes.
Drizzle lemon juice over leek mixture; season with salt and pepper. Cover pan and cook over low heat until leeks are tender, 15 to 20 minutes.
