According to Ableton’s site,
“A regular Live license is intended for a single user and cannot be shared.
Each license covers the use of the software on two active computers owned by the registered user.
A new authorization may become necessary in the event of replacing essential hardware components (motherboard, hard drive, graphic card, etc.) or after an operating system reinstallation. In such cases, you will be informed by an automated email to your registered address and additional authorizations can be requested from your user account.”