This soup is also wonderful served cold or at room temperature with a dollop of sour cream.
Melt butter in a small stockpot over medium-low heat. Add the shallots, parsnips, celeriac, carrots, and salt and pepper to taste, and saute until the shallots are translucent, 5 to 7 minutes.
Add the chicken stock, tarragon, and 1 1/2 cups water; bring to a boil. Reduce heat to medium low; simmer until vegetables are al dente, 5 to 6 minutes. Add beets; cook until vegetables are tender, 15 to 20 minutes. Remove and discard tarragon sprigs, and stir in lemon juice. Serve immediately, garnished with dill.