HMark,
I've grilled lobster tails a couple of ways. The key is to cook over medium, indirect heat. Baste the tails frequently with a garlic butter sauce, seasoned to your preference (I like a little old bay seasoning or cayenne). This will keep the meat from drying out. Also, try to prevent flare ups, as this will tend to dry out the meat.
So, you can split the tail completely in half vertically, or simply cut open the top half of the shell. I've done it both ways, and as long as the butter sauce is applied every couple of minutes after the first turn (while the meat is exposed topside, away from the grill), the meat retains a moist, juicy texture. You should apply some butter sauce just before placing them on the grill, as well.
Three to four minutes on one side, turn, and four to five minutes on the other side, or until the meat is opaque.
I haven't used a smoke box on lobster. I'd imagine Applewood might be good.