Thoroughly peel the white asparagus. Save the peels and woody ends. Cut off the tips (approx. 3-4 cm) and set them aside. Cut the remaining asparagus stalks into pieces about 2-3 cm long.
In a pot, bring the water with the asparagus peels and ends, salt, sugar, and a quarter of a lemon to a boil and let it simmer for about 15-20 minutes, then let it steep for 10 minutes.
Strain the resulting stock through a fine sieve and discard the solids. Set the stock aside.