Thanks @AnotherElk and @oli.sax !
Both solutions work very well.
At least the last one was probably too easy. 
I did not notice that the internal storage is also visible (e.g. in the OS File Explorer/Manager - “Nautilus”/“Files” in case of PureOS or other Linux OS with GNOME Desktop) when you boot into TWRP.
Also the sideload is pretty easy:
In TWRP go to Advanced → ADB Sideload (and active via slider so that the phone is ready to receive a zip on this way)
Then simply go to the folder where you stored the zips on your PC and execute the adb sideload filename.zip
E.G. here I wanted to zip a nightly and the su addon zip (you have to reactive sideload in between):
<path_to>/LineageOS_zips#
adb sideload lineage-15.1-20181029-nightly-FP2-signed.zip
Total xfer: 1.00x
adb sideload addonsu-15.1-arm-signed.zip
Total xfer: 1.73x