Make sure you use the current TWRP version from twrp.me as advised in the LineageOS installation guide. The older TWRP version bundled with Fairphone’s OSes is known to cause some trouble here and there.
A “factory reset” on the Fairphone 2 will delete user data and Apps installed by the user (yeah, it is not a factory reset in the sense of the term), the OS will be left as is and upon the next boot will restart the initialisation process as if it was newly installed (which it wasn’t).
“Format Data” goes a step further than wiping does. Formatting data doesn’t only delete files, it really formats the data partition. Not only all user data will be gone, but if the data partition was encrypted (that’s what encrypting “the phone” really does), encryption will be gone, too.
Formatting Data also will not touch the installed OS.
If you want to play it safe and really install from scratch, here’s how … for Fairphone’s OSes anyway, but you can continue installing LineageOS after the “Format Data” part in the guide …