Welcome back to the Wefugees Community and thank you for reaching out to us again.
Unfortunately, I am not familiar with the immigration/residence procedures in Luxemburg. However, I think you can find many information on this official/governmental website. Apparently, there is also an option for non-married but long-term partners to apply for a respective visa. In any case, I would recommend your partner in Luxemburg to get some individual counselling there, as people will be more familiar with the specific rules/laws.
I hope this helps and all the best,