Snap off the bottom third of each asparagus spear and put the bottom portion of the spear in a large saucepan. Add the chicken broth to the saucepan. Bring to a boil and then simmer, tightly covered for 30 minutes. Discard the stalks and set broth aside.
Cut the upper asparagus spear tips into about 1 inch pieces.
In a large frying pan, melt the butter and then add asparagus spear tip pieces, onion, leeks, celery, and potato. Cover tightly and over low heat cook the vegetables for about 20 minutes. Cool slightly.
In batches puree the vegetables with some of the asparagus infused chicken broth. Add lemon juice and salt and pepper to taste. Garnish with asparagus spear tips.
The soup can be served warm, room temperature or chilled.