Instagram can save all live broadcasts in a section called Live Archive.
You can enable or disable the automatic saving of your live broadcasts via the Instagram app:
If you enabled automatic saving, then all lives that were streamed via Loola will be saved to the Live Archive.
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