Place lobster tails (in shells) in a boiling pot of salted water. Boil for about 5-7 minutes (depending on the size of tails) until the lobster tail turns bright red and the inner meat is no longer translucent and turns white.
Remove lobster tail from water and allow to cool in a colander. Remove fins from the end of the tail. Lay tail on counter and press down firmly on the outside of the shell to crack it. Remove meat with a fork. Cut lobster meat into chunks and set aside.
Note: It's okay if you find the lobster is not fully cooked after chopping it. It will cook through when added to the soup later.
In a large pot set to medium-high heat, add butter. Once melted, add carrots, celery, onion, and garlic. Cook 7-8 minutes until vegetables are softened. Stir in tomato paste and cook for 1 minute. Add flour and stir vegetables to coat.
Slowly add wine and stir to blend. Add salt, pepper, thyme sprigs, bay leaves, chicken broth, and seafood broth (or reserved lobster water) and bring to a boil. Reduce to a simmer and let cook for 15 minutes, stirring occasionally.
Remove thyme sprigs and bay leaves from pot. Using an immersion blender, blend soup until all vegetables are pureed and soup is smooth. Add heavy whipping cream and lobster meat and cook for an additional 5 minutes at medium-low heat.