Preheat the oven to 325 degrees F. Put the rib racks on a work surface bone-side up. Slip a knife between the bone and membrane, then pull off the membrane. Cut each rack of ribs in half; season evenly with 1 teaspoon salt and 1/2 teaspoon pepper. Heat the olive oil in a large Dutch oven or pot over medium-high heat. Add the ribs, bone-side up, and sear until brown, about 5 minutes. Remove and set aside.
Lower the heat to medium, add the celery, carrots and onion and cook, stirring, 5 minutes. Stir in the chopped garlic and tomato paste; cook 2 minutes. Add the beer and bay leaf, bring to a simmer and cook until reduced by half, about 5 minutes. Return the ribs to the pot, add the chicken broth and bring to a simmer. Trim a piece of parchment paper to fit the pot, then place directly on top of the ribs and cover with a lid. Transfer to the oven and braise 1 hour, then remove the lid and parchment. Continue braising until the ribs are tender, 45 minutes to 1 hour more.
Meanwhile, put the potatoes in a saucepan and cover with water by 1 inch. Bring to a boil and cook until tender, 15 minutes; drain.
Remove the rib racks from the pot; let cool slightly, then cut into the ribs. Strain the cooking liquid, discarding the solids; skim off some fat. Return the liquid to the pot.
Add the smashed garlic and tomato to the pot and bring to a simmer over medium-high heat. Add the clams, cover and cook until some just open, 5 minutes. Add the potatoes and ribs, cover and cook until all the clams open, 10 to 15 more minutes (discard any unopened clams). Stir in the parsley and lemon juice. Serve with lemon wedges.