You can buy the local lobster (also called Omani lobster). IMHO I don't care for it, it is not the same as lobster from the North Atlantic.

Very occasionally, C4 has Canadian lobster, I am wary of it as well as it is usually dead. In my part of the world, no one would buy a raw,dead lobster. You could go to C4 and see if any of them are moving, they are very expensive though.

Even more occasionally I've seen small cooked frozen lobster (whole) at Megamart, but not recently.

Sorry not to be of more help.