For the béarnaise sauce: Add the wine and shallots to a saucepan over medium heat and bring to a simmer. Let simmer until the wine mostly evaporates. Then set the pan aside to cool. In a bowl whisk the egg yolks and lemon juice; season with salt and pepper. Mix the shallot wine reduction with the egg yolks. Slowly drizzle in the melted butter while whisking. The sauce should become thick and smooth. Whisk in the tarragon. Set aside.
Season both sides of the steak with the steak seasoning, salt, and pepper.
Preheat a grill or grill pan on medium heat.
In a pot of boiling water cook the lobster to an internal temperature of 135°F using a thermometer. Drain and remove the shell. Chop up the lobster meat and season with salt and pepper to taste.
Cook the steak to your desired temperature using a thermometer (see below).
Set the steak on a cutting board to rest for 3-5 minutes.
Top the steak with lobster meat and spoon the béarnaise sauce over. Garnish with tarragon.