Can I run a user test with Lookback through the mobile app?

Only the InVision iOS app has the Lookback feature. At this time, the Lookback is only available for iPhone and iPad.

Lookback does make available an app for using their service on Android devices that may be of help, but it's not specific to InVision.

The InVision iOS app also lets you view screens from Apple Watch prototypes on an actual Apple Watch. However, at this time the screens are not interactive and you can only swipe left and right to switch screens.