I was hurt in a car wreck caused by someone else. At the timeof the accident, my automobile insurance had lapsed. Can I still recover compensation for my losses and injuries?

The fact that you did not have insurance at the time of the car accident will not impact your ability to recover.  If the collision was the fault of the other driver, your claim is with the other driver's insurance compnay.  You may be able to recover for your medical expenses, lost income and for pain and suffering.  Be aware, however, that the insurance company will be difficult to deal with.