If you don't get a permissions dialog in the Chrome extension, it can be because the extension was blocked from accessing the microphone and/or camera sometime earlier.
Follow these instructions to get the permission dialogs back.
1. Close any Lookback chrome extension popup
Tip: If you can't find the popup, the extension icon in the URL bar will bring it to front. If you didn't have a popup, it just launches a help screen that you can close straight away.
2. Open the "Clear Browsing Data" dialog
From the "three vertical dots" you will find the Clear Browsing Data option from "More Tools".
3. Clear cookies and site content
In the dialog that opens, chose:
All time (to definitely cover the time period when the access was blocked)
"Cookies and other site data"
Then click the "CLEAR DATA" button at the bottom.
4. Relaunch the Lookback Chrome extension popup
Using whatever method you previously used to start the the popup. More info here.