Bought my lease a year into my contract and turned around and sold to Carvana for profit. Short or long term?

This will be a short-term capital gain as from what you stated you did not actually own the car until you purchased it from the leasing agency.  The date of acquisition will be the date on the sale/transfer agreement from the leasing agency and the date of sale will be the date you and the ultimate purchaser signed the subsequent agreement.  

Be sure to add any title and transfer fees to the basis of the car when you purchased it officially and any assessed when you sold it as they may lessen any gain you may have. 

The sale should be reported as a short-term gain on Schedule D.  The actual rate of capital gain tax you will be subject to is based on your overall income but the majority of taxpayers fall into the 15% category.  For further information, the links below should prove useful.

How is a capital gain or loss calculated?

Capital gain or loss per the IRS

@Jose0