What app are you using specifically? Normally, it's not the GPS itself that is using up power, but the mobile data needed either for live traffic updates or for downloading maps in case you haven't downloaded them to your phone yet.
Also, it's not the input power/voltage/ampere rating that matters but rather the output rating of the charger. 12V is most probably the input rating of the charger, e.g. in car phone chargers, since 12V would most definitely fry your phone if it was the output of the charger. You may want to use a 2A and 5V output charger for your L1020.
In my L1020, using a power bank that has a maximum* output of 3.6A can still charge my phone despite it using GPS and data at the same time, i.e. for the Waze app.
*- May not be the actual output it gives the L1020. I think that my Sony powerbank supplies power to the phone such that it can charge the battery at or near 2A (just like the default charger). Hence, if the phone is using more power than when it is in standby, my powerbank may be delivering more than 2A to compensate for the additional power demand.