How would it otherwise? Network based location?
Yes. Your phone could triangulate its location from nearby celltowers ane wifi networks. Google has a database of wifi routers (actually that was the point of google streetview, they collected wifi bssids alongside taking photos, they also collect this data from android devices).
With microg you can select from different dbs for this, they are called 'UnifiedNlp backends': apple has a similar db from iphones, mozilla used to collect this data with a separate app for MLS (they shut down the project in 2024 march). Microg builds an on device private db as well, it will remembers the wifi networks and celltowers you were close to, and next time you are there it won't need gps, saves a ton of battery life. This was called Deja Vu, I love this name. Search for UnifiedNlp on fdroid you can find some more options.
Since MicroG 0.3 you don't have to install these separately, Mozilla and Deja Vu are builtin, and they are more than enough
Why don't you just reflash the LOS image? You can get into bootloader, right? If you are there, just
fastboot flash
the LOS image: https://wiki.lineageos.org/devices/dubai/install/#flashing-additional-partitionsThan you should get to the LOS recovery, from there you can wipe? Or do you need authorization for fastboot as well like for adb?
Or is it a requirement that you need data from the phone?