Recently, Instagram released a new feature called Live Archive. As part of the new feature release, Instagram removed the option to save the Live to the Story.
All lives that were streamed via Loola are saved to the Live Archive by default.
You can select a saved live from your mobile Instagram app and share it to IGTV (only if it's longer than 15 minutes).
To view your Live Archive open Instagram on your mobile device and select:
Profile --> Menu --> Archive --> Live