Yes a pregnant woman can eat lobster.
Lobster which is considered shellfish is safe for pregnant woman to eat during pregnancy.
Just make sure the lobster or any other shellfish you eat during pregnancy is fully cooked to avoid any potential bacteria causing harm to yourself or your unborn baby.
I've eaten lobster during pregnancy and even eaten other shellfish during pregnancy and my babies turned out just fine and I had no complications during my pregnancy or with my pregnancy.
My babies which are now kids are all healthy and full of energy.
I wish I could be as full of energy as them.
So as long as you cook the lobster fully or you get the lobster cooked from a lobster place then it will be safe to eat during your pregnancy.