Preheat the grill to 450° to 500°.
Herb Butter: Add the softened butter to a standing mixer with the paddle attachment and whip on high speed until it becomes light and fluffy, about 5 to 7 minutes.
Next, add in the shallots, garlic, lemon, herbs, salt and pepper and whip on low speed.
While the butter is whipping add in the honey so that it integrates into the butter immediately.
Remove from the standing mixer and transfer to a plastic container and chill in the refrigerator. Note: there will be a lot of leftovers.
Lobster: brush the meat side of the lobster with olive oil and season with salt and pepper.
Place the lobster meat side down onto the grill and cook for 3 to 4 minutes per side.
Once you flip the lobster over generously spread on some of the herb butter on the grilled meat side.
Next, immediately put the lemons cut side down onto the hot grill and cook for 2 to 3 minutes or until there are grill marks.
Remove everything from the grill and transfer to a serving platter and garnish with microgreens.