Is Satan capable of love? Is Satan capable of love?
It does not matter what name we give to the leader of the fallen angels: Satan, Lucifer or the Devil. What I desire to know is if the leader of the fallen angels, commonly known as Satan is genuinely capable of love?
For this question, I desire an overview of what various Christian denominations teach (defined or undefined, official or unofficial) on this subject matter, such as Catholicism, Orthodox, Lutheranism, Anglicanism, etc.
For a Catholic perspective, Pope Francis, who talks about Satan as much as he talks about anything else says that Satan does not know how to love.

The second attitude is that of Herodias, the wife of the king’s brother. “The Gospel says that she ‘hated’ John” because he spoke with clarity. And, the Holy Father continued, “we know that hatred is capable of anything”. Indeed, “hatred is the breath of Satan”, who does not know how to love”. Herodias “had the satanic spirit of hatred”.
http://www.vatican.va/content/francesco/en/cotidie/2019/documents/papa-francesco-cotidie_20190208_greatgift-ofmartyrdom.html

If you don't know how to do a thing, it doesn't mean you're not capable, it just means you're not apt to do it.

A reformed perspective is more pragmatic, playing a little loose with the word love:

It makes sense that Luther would have such a strong experiential knowledge of the devil, for Satan loves nothing more than to attack the gospel, and Luther was at the forefront of the greatest recovery of the gospel
https://www.ligonier.org/learn/devotionals/our-enemy-devil/

So Satan, if he does love, he loves doing evil.  The meaning of the word love in that case would be about the basest possible meaning of love that I don't even know how it qualifies.

I don't believe that the Orthodox have a particularly extensive demonology department, which is probably to their credit! It might be hard to find an answer there.