Heat your bbq till it gets nice and hot with one side on full and the other on low.
Mix the butter, shallot, lemon juice, garlic, thyme, chives and salt in a bowl. Set aside. Take out about 1/4 cup of the mixture if you want to dip your lobster in it later when you eat it.
Wash your lobster tails really well.
Cut your lobster in half lengthwise, especially if you have jumbo tails. Or if you prefer, you can leave them whole and just cut down the center of the top shell and a little bit into the flesh to butterfly it.
You will want to find the dark line running from head to tail and remove it. Its nothing you want to eat!
Place the lobster, flesh side down on the hot side of the grill for about 2 mins or until you get some nice grill marks. Then flip the lobster over and place on the low heat side, shell down, for about another 5 mins for regular sized tails and 8 to 10 for jumbo sized.
Baste with the lemon herb butter every min or so to get that butter really soaked in and down all the cracks. YUM.
Remove from heat and serve immediately with some of the reserved lemon herb butter or with just regular melted butter for dipping.