Thanks SethGeckoXDA for the super fast reply. I tried what you said - regarding the airplane mode I have tested it before and that effectively prevents battery drain (~80% battery left after a day without much usage) thus I would assume the drainage is caused by any of the connections to the outside - Wifi, Bluetooth, mobile service, you name it. Today I set the phone to 2G only but that did not help. Tonight the phone is pretty much dead (2% battery left). Again I would be happy to help, as it is currently the only phone that I own and is working.
If you have not done it already, you can now try turning off all other services (WiFi, Bluetooth, GPS, ...) to determine if only the mobile network service is actually the culprit.
If mobile network is responsible for most of the battery drain, it can either be
- a bug in the firmware or LOS keeping the device busy.
- or a wakelock caused by one of your installed apps.
If you don't mind putting in some work and doing clean flashes, you can try:
(1) installing only LineageOS (clean flash),
(2) then installing LineageOS + GApps (clean flash)
(3) and finally LineageOS + GApps + your usual apps (clean flash + install your apps one by one to determine the culprit).
In all of the three installs, let the phone rest for some time with mobile network enabled and see if the battery drain occurs.
If the battery drain happens in case (1), it obviously is a bug in either the firmware or LOS.
If the battery drain occurs in (2), you could try another version of GApps (OpenGApps, mindTheGApps, ...)
If it happens in (3), either remove or properly configure the apps which cause the drain.