Once your lease has expired, your status as an Authorized User will be removed from the credit card(s). However, most credit card companies tend to leave the account history on your credit report for a period of six months to several years.
The long-lasting benefits of these accounts give you the ability to access more favorable financing and employment options. It will also make it easier to continue improving your credit score over time, though you may be able to continue making improvements while paying lower interest rates than you were previously.
It is important to note that the credit card company may remove the information from your report as soon as you are removed as an authorized user. In that regard, it is often best to avoid procrastinating if you were hoping to qualify for a new line of credit on your own. If your intention is to continue improving your credit score, then the loss of the credit card(s) from your credit report will have a less notable effect on your plans.