Which particular app are you using?
Most probably, it is the screen that was contributing to most of the battery drain. If you're app is constantly using internet data (such as Waze for live traffic updates), then that's also a major battery drainer. Aside from these two, the GPS antenna also contributes to battery drain but not as much - the proof of this is that when using a track logger that uses GPS under lock screen, my battery doesn't drain as fast as compared to when the screen is turned on (battery drain under lock screen for GPS only is around 10% per hour).
That the screen and mobile data antennas consume a lot of power are applicable to almost all smart phones, so if you would be using these two while navigating (check if your app uses data while it is active), you would want to connect your L1020 to a portable power supply, e.g. a power bank.
I've never left my house without a power bank - got myself a 10,000 mAh Sony power bank with a max output charge rate of 3.6A (but I think the L1020 can only take around 2A, so 2A should be enough). :wink: