The fourth hurricane of the 2002 can threaten the Louisiana or upper Texas coast by early Thursday.
Though it is too early to tell where Lili might come ashore in the United States.
Lili was upgraded Monday from a tropical storm to a Category 1 hurricane and its maximum sustained winds have strengthened to 80 mph.
Lili is potentially more dangerous than Isidore, as Lili is going to just skirt the western tip of Cuba. It's not mountainous there. It's relatively flat. So it could go ahead and strengthen over the warm waters of the Gulf of Mexico.
The region's biggest producers Royal Dutch/Shell Group's Shell Oil Co, BP Plc and ConocoPhillips Corp. all started to move oil and gas workers out of harm's way.