Wash the asparagus, drain and cut off the ends. Wash the lemon and thyme, halve the lemon and shake the thyme dry.
Press the garlic cloves flat with a knife, rub off the shell of one lemon half and then cut the half into slices.
Preheat the grill and place the asparagus, garlic, slices of lemon and thyme on it. Spread approximately 2 tablespoons of the olive oil over it and then grill the asparagus with not too much heat.
Just before the end, add the remaining olive oil and the lemon zest and season with salt and pepper.