Without getting into specifics of which ROM you are currently using and which one you want to flash, TWRP isn’t a good idea. Reasons :
TWRP is used to make a nandroid image and as you can see from the nandroid tag wiki help, you may run into serious issues if the directory structure of the ROM is different. Restoring a section of TWRP backup may also cause problems (read the linked page for details).
What may be a user app in one ROM, may well be a system app (having elevated privileges) and this may cause trouble.
Google dependencies : You may be running Gapps on Lineage and this may not be possible in other ROMs.
I am not familiar with Ubuntu but I doubt you would be able to run most user apps from LineageOS on that.
There would be more reasons, but these occurred to me on reading your question. You are better off making individual backups of apps using titanium-backup and restoring these as per your need.
Recently, I was doing some research on backup apps since Titanium failed for me on Android 11,and I came across this app, specifically designed for frequent ROM flashers and this may fit your need better. See Migrate-custom migration tool
Move apps, data, contacts, SMS etc from one custom ROM to another.
Interestingly, it claims to restore app permissions too. XDA thread here and Telegram here. You need TWRP to use this app.
I haven’t tried this app (don’t need it) nor am I affiliated with it.