Heat oil in a frying pan over medium heat. Cook and stir garlic in hot oil until fragrant, about 1 minute; add asparagus and season with salt. Cover pan with a lid and cook, stirring occasionally, until asparagus is tender, 3 to 5 minutes. Let asparagus cool in the pan.
Arrange egg quarters beside the cooled asparagus; season with pepper and garnish with lemon slices.