Thaw lobster tails, if frozen.
Place thawed lobster tails on a cutting board or working surface.
Using kitchen shears, cut straight along the center of the top of the lobster shell, cutting towards the fins of the tail, but do not cut through the fin. Gently open up the shell and run a spoon between the meat and the shell to loosen it up.
Open up the shell, carefully so you don’t break it, and pull and lift the lobster meat off the bottom of the shell, but do not remove it.
With a knife or kitchen shears cut halfway through the meat down the center, but do not cut all the way through.
Melt 1 tablespoon butter and brush the lobster tails with the butter.
Season the lobster tails with salt and pepper.
Place the lobster tails in the air fryer basket and cook at 380˚F for 5 to 7 minutes, or until the lobster meat is opaque and cooked through.
In the meantime, prepare the sauce and melt remaining 2 tablespoons butter in a skillet.
Add shallots to the skillet and cook for 1 minute.
Stir in the garlic and parsley and cook for 20 seconds while stirring.
Reduce heat to medium-low.
Stir the heavy cream into the skillet.
Add the parmesan cheese and bring sauce to a simmer; continue to cook for about 1 to 2 minutes, or until slightly thickened.
Whisk in the lemon juice.
Taste and adjust with a little salt and pepper, if needed.
Remove from heat.
Serve sauce with lobster tails.