It's your responsibility to arrange insurance for your lease car from the day that it's delivered until your chosen provider collects it.
Because the finance provider is the registered owner and keeper of the vehicle, they will more than likely require you to choose a fully comprehensive policy, which will cover damage to other people's property, you and your car, and any passengers if they get injured.
For personal leasing, the insurance must be in the name of the person who is the main finance holder. For business leasing, this needs to be in the company or director's name.