As we lose weight should our pulse decrease, even if we aren't very active? Lost 121 lbs in five months. Recently my pulse has been between 50-66

To me it's a "yes, but" type question. Yes, no doubt your pulse and blood pressure will go down when you drop a lot of weight. It will go down even further if you work out.

But, you should ask your doctor. You want to make sure your pulse and//or blood pressure aren't too low for another reason.