Can I sue a car dealership for almost getting me killed because they didn’t tighten lug nuts?

You could sue the auto dealer for negligence.  Negligence is the failure to exercise due care (that degree of care that a reasonable auto dealer would have exercised under the same or similar circumstances to prevent foreseeable harm).  If you did NOT have any property damage to your vehicle and/or personal injury to yourself or other occupants of your vehicle, you will recover little or nothing.

If you had property damage to your vehicle and/or a personal injury claim, you will have a strong case for recovering damages (monetary compensation) for negligence in your lawsuit.

In order to prove negligence, you will need to prove duty (of due care mentioned above), breach of duty (failure to exercise due care by not tightening the lug nuts), actual cause, proximate cause and damages.

Actual cause means but for the auto dealer not tightening the lug nuts would you have been injured or would your car have been damaged?  If the answer is no, actual cause has been established.  Proximate cause means were there any unforeseeable intervening acts which would relieve the auto dealership of liability?  If the answer is no, proximate cause has been established.  Damages means the amount of compensation you are seeking to recover in your lawsuit.  Your damages would be the cost of repairs to your vehicle and your personal injury claim.  As for the property damage to your vehicle, you will need to mitigate (minimize) damages by having the car repaired at an auto body shop whose charges are comparable to other auto body shops in the area.  If you were to select the most expensive auto body repair shop you could find, your damages would be reduced accordingly.  If you need a rental car while your car is being repaired, you will need to mitigate damages by selecting a reasonable rental car rate.  If you were to select the most expensive rental car you could find, your damages would be reduced accordingly.

As for your personal injury claim, when you complete your medical treatment and are released by the doctor or are declared by the doctor to be permanent and stationary which means having reached a point in your treatment where no further improvement is anticipated, obtain your medical bills and medical reports.  Compensation for the medical bills is straight reimbursement.  The medical reports will document the nature and extent of your injury and will be used to determine compensation for pain and suffering which is an amount in addition to the medical bills.  Your damages should also include compensation for wage loss.  Compensation for wage loss is straight reimbursement.  Prior to filing your lawsuit for negligence against the auto dealer, it may be possible to settle the case with the auto dealer's insurance carrier.  If the case is settled with the insurance carrier, NO lawsuit is filed.  If you are dissatisfied with settlement offers from the auto dealer's insurance carrier, reject the settlement offers and file your lawsuit for negligence against the auto dealer.  If the case is NOT settled with the auto dealer's insurance carrier, you will need to file your lawsuit for negligence against the auto dealer prior to the expiration of the applicable statute of limitations or you will lose your rights forever in the matter.