Thaw the lobster completely if using frozen lobster tails. Remove the meat from the shells and cut it into bite-sized pieces. Pat the lobster dry with paper towels.
Heat the olive oil or 2 tablespoons of butter in a large skillet over medium-high heat.
Add the lobster pieces in a single layer. Season lightly with salt and black pepper. Cook for about 2 to 3 minutes, turning once, until the lobster becomes opaque and just cooked through. Avoid overcooking to keep the meat tender. Transfer the lobster to a plate.
Reduce the heat to medium. Melt the remaining butter in the same skillet.
Add the minced garlic and cook for about 1 minute until fragrant, stirring frequently to prevent burning.
Pour in the seafood broth and let it simmer for about 2 minutes, allowing the flavors to concentrate slightly.
Stir in the fresh lemon juice, thyme, and optional red pepper flakes.
Return the Garlic Butter Lobster Bites to the skillet and gently toss until every piece is coated in the buttery garlic sauce. Cook for another 1 to 2 minutes.
Taste the sauce and adjust the seasoning if needed.
Sprinkle with fresh parsley and serve immediately with lemon wedges.