Reduce heat to medium, cover and simmer until asparagus is tender, about 8 minutes.
Add spinach, cover and simmer until wilted, about 4 minutes.
Puree mixture in a food processor.
Mix lobster meat, shallot, and 1 tbsp of lemon juice in a medium bowl. Season to taste with salt and pepper.
Mix avacado and remaining 1 tbsp of lemon juice in another medium bowl and mash coarsely. Season with salt and pepper. Pack a Timbale with lobster, cavier, and avacado mixture and place in the middle of soup.