Preheat your oven to 350°F (175°C).
Prepare the lobster tails by using kitchen shears to cut down the center of the shell and gently pull the meat up, resting it on top of the shell.
In a small saucepan, melt the butter over low heat. Once melted, add the minced garlic, chopped parsley, lemon juice, salt, and pepper. Stir to combine and let it simmer for about 2 minutes. Remove from heat.
Place the lobster tails on a baking sheet and generously baste them with the garlic herb butter mixture.
Bake in the preheated oven for 20-25 minutes, or until the lobster meat is opaque and slightly firm to the touch.
While the lobster tails are baking, prepare the mashed potatoes. Peel and cut the potatoes into chunks. Place them in a pot of salted water and bring to a boil. Cook for 15-20 minutes or until tender.
Drain the potatoes and return them to the pot. Add the butter, milk, salt, and pepper. Mash until creamy and smooth. Adjust the consistency by adding more milk if desired.
Once the lobster is cooked, remove it from the oven. Serve the lobster tails alongside a generous scoop of mashed potatoes. Drizzle any remaining garlic herb butter over the top for extra flavor.