Using kitchen shears, cut down the center of each lobster tail shell. Remove the lobster meat in one piece. Remove the dark vein if present. Pat dry with paper towels and season lightly with salt, pepper, and paprika. Keep the tails whole.
Heat a skillet over low to medium-low heat. Add 5 tablespoons unsalted butter and 2 smashed garlic cloves. Let the butter melt gently without browning.
Add the whole lobster tails to the butter. Cook slowly, flipping occasionally, for 5-7 minutes. Target an internal temperature of 135-140°F. The lobster should be opaque, tender, and slightly firm.
Lower the heat slightly. Add honey, chili crisp, apple cider vinegar, and a pinch of salt directly into the butter. Stir gently until combined into a glossy sauce. Toss the lobster in the sauce until coated.
Remove the pan from heat. Squeeze fresh lemon juice over the lobster. Let rest 1 minute, then chop into large, chunky pieces.
Slice King's Hawaiian rolls in half. Butter the cut sides and toast in a skillet over medium heat until golden brown, about 1-2 minutes.
Add optional lettuce to each roll. Load generously with chunky lobster. Spoon extra hot honey butter from the pan over the top. Finish with chives or parsley and lemon zest. Serve immediately.