Your Live license allows you to install and authorize/unlock Live on two computers, with the understanding that you will only have two computers authorized at any one time. To put Live on a second computer, take the following steps:
1. On the new computer, log in to your User Account at Ableton.com
2. Download the latest version of Live (make sure you have the right license selected)
3. Install Live
4. On first launch, you will be prompted to authorize at Ableton.com
Please note: you will need to be logged in with the email address your license is registered to in order to access your software.
Re-entering your serial number will not authorise Live, only register it again or show the error "already registered to another user" if you're logged in with a different account from the one your license is registered to.