Wash the asparagus, cut off the woody ends and cut the asparagus into pieces. Rinse lemons hot, peel in zests. Halve lemons and squeeze juice. Cut bread into very thin slices.
Heat the fat in a frying pan and fry the slices of bread until crisp, turning them over, then drain them on kitchen paper.
Prepare the pasta in boiling salted water according to the instructions on the packet. Simmer cream and lemon juice in a pot for about 3 minutes, season with salt and pepper, add about half of the peas, let simmer for 1-2 minutes, puree sauce, stir in remaining peas.
Heat the oil in a pan. Sauté the asparagus for about 4 minutes, turning it over, and season with salt, pepper and sugar. Crumble bread slices between your hands.
Wash herbs, shake dry and pluck leaves from the stems. Drain the pasta, mix the sauce and asparagus, arrange on a plate and sprinkle with crumbs and herbs. Garnish with the lemon halves if desired.