Whether you've purchased the product outright, or have just completed your Bitwig Studio Rent-to-Own plan, a product serial key will be sent to your Splice email. You will then need to activate your lifetime license through your Bitwig account. (You should have created a Bitwig account when you started your plan. Find more information here.)
Log into your Bitwig account here then navigate to Account Info. You will be able to enter and activate your lifetime license key on this page. Once, you've taken these steps, you will no longer need to involve Splice in launching or utilizing the product.