The FP2 is 1,5 years old. Just because it’s fair doesn’t mean it ages twice as fast as other phones. 
Well that’s the question that has been around since the FP2 was announced to be modular, e.g. here.
Fairphone always said that the main goal of the modularity was an increased repairability and it was not so much about upgrades. However they did upgrade the cover and are (still) working on a camera upgrade.
Judging by the fact that the camera upgrade seems to take ages and they are now concepting an FP3 I’d guess they are not planning/able to upgrade the main module.
However FP2 is not stuck on Android 6 like FP1 is stuck on Android 4. The only thing keeping the FP2 on Android 6 is Google’s official Support - which the FP1 never had. As soon as that is ditched (either by you - installing Sailfish, or by Fairphone - no longer working on FP OS but only Open OS) you’ll have Android 7 on your Phone.
If you just purchased your FP2 last week there can’t be a lot of important Data on it yet that you can’t loose and even if: You can always do a dic:backup before testing Lineage OS (or other) and come back if you don’t like it. The forum is full of guides and helpful people that can teach anyone how to flash a different OS/ROM.
Google’s official support is only there for two reasons: to be allowed to have GAPPS pre-installed and to get timely Android Security Upgrades. Since LineageOS and @chrmhoffmann provide monthly security updates (at least it looks like it for now - the port is still very fresh), you won’t need official support.
Fairphone never said that. It could theoretically still be possible. Maybe they’ll start working on it after FP3 is released.