Fill a large stock pot two-thirds full with water. Add the crab boil seasoning bag, halved lemons, and halved garlic head. Bring to a rolling boil over high heat, about 10–12 minutes.
Add the red potatoes and boil for 12–15 minutes, until just fork-tender.
Add the sliced sausage and corn pieces. Boil for another 6–8 minutes.
Add the shrimp and cook for 2–3 minutes, just until opaque and curled.
Drain everything in a large colander. While it drains, whisk together the melted butter, cajun seasoning, minced garlic, smoked paprika, lemon juice, and hot sauce.
Transfer the drained boil into a large zip-top bag or lidded cooler. Pour in the butter sauce, seal, and shake vigorously for 30–45 seconds until everything is evenly coated.
Dump onto a platter or lined table and serve immediately.