In a casserole, heat oil at medium heat. Add onion and tarragon, and cook, stirring from time to time, for about 3 minutes or until onion has soften. Add rice and stir.
Add vegetable stock, water and salt. Reduce to low heat, cover and let simmer for 15 minutes. Add asparagus, cover and keep cooking for about 10 minutes or until rice is tender and liquid has absorbed. Add lemon juice and pepper and stir with a fork.