Because you're the not-at-fault driver, you would be filling a claim through the other driver's insurance policy. I definitely would repair the damage before you contact your lease,
as the damage is probably a violation of your lease agreement. If you're filing with the other driver's insurance company, you would not be paying your deductible. Moreover, this accident shouldn't affect your insurance premium going forward as you were not-at-fault at the time of the accident.