Break off the woody ends from each asparagus spear, discard them and cut the rest into 1 inch pieces, leaving the tips intact. Keep the tips separate from the rest of the stems.
Melt the butter in a medium-size heavy saucepan, add the onions and sauté them for about 3 minutes. Do not brown them. Add the asparagus pieces and cook them for a couple of minutes. Add the flour and sauté for another couple of minutes. Whisk in the chicken broth one cup at a time. Add the milk, salt, pepper and nutmeg, bringing it to a boil, then simmer covered for about 10 or more minutes. You want the asparagus to be very soft.
Puree the soup with an immersion stick or in a mixer.
Reheat the soup and add the half and half, season with additional salt, pepper, and lemon juice.
In the meantime cook the asparagus tips in boiling water for about 2 minutes. When you serve the soup add the asparagus tips to the individual serving bowls.