When cooking a large lobster tail, the trick will be to cook it all the way through without scorching or drying out the top. If you do cook it too long, the meat will be tough and chewy.
The best way to approach broiling a large lobster tail is to first thaw it, then cut open the top of the shell lengthwise. You will need a heavy pair of kitchen shears to do this, and you will want to cut just deep enough that you do not cut the bottom of the shell. You may need to use a large knife to cut through the meat and you will then need to split the shell open. Then, you will put it in a roasting pan just underneath the broiler. Cutting the lobster tail open like this will help expose the meat to the broiler so that it will cook evenly and prevent the shell from burning or drying out.