Continuing the discussion from Official LineageOS for Fairphone 3:
Question: how about Android 10? Does LineageOS 17.1 for microG on FP3 run on 9, like the previous? Should I wait for further development before upgrading my FP3 from Lineage OS 16.0-20201210-microG-FP3 to the new 17.1?
No, see: LineageOS - Wikipedia
It seems to work quite well already, if I understand the quoted discussion correctly.
I used that prior to the update available by Jan 27 2021, without any implications. Be aware, that the /data partition (and by that all user installed apps and their data) will most probably be lost during the update (at least if you come from LOS 16+microG).
Thank you, so I finally dared starting the process, and guess what now my FP3 shows “Lineage OS 17.1” and “Android 10”, so apparently the upgrade from Pie to Q came automatically with the Lineage OS upgrade. And now I am restarting the process of customizing my phone - I get quite experienced by doing this time and again! But after reading a lot in the forum I decided against rooting and system backups like with TWRP or magisks. That would outstrip my skills. So I only backed up my data.
Congratulations on that! 
By the way, in LOS 17.1, there is a built in backup tool hidden in the menu, which can help backing up your apps. It’s called Seedvault Backup, hidden under System / Backup (I guess, my interface is set to German language). Be aware that without root, it can only backup app which allow being backed up…