... on whether the Lutheran Antipope is Lutheran?

It would seem that he is:

The Lutheran Antipope
vaticancatholic.com
https://www.youtube.com/watch?v=Zg7M_FwLF7E

But on the other hand I answer one should say:

I suppose that was the kind of modernist, Lutheran friendly Novus Ordo Catholics who delayed my conversion.

I decided to convert at age 16, after reading Umberto Eco and finding out Albigensians weren't exactly Bible Christians, and Waldensians were Anarchist to Commie types, I was only allowed to convert a few months before "excommunication" of Mgr Lefèbvre - at age 20. OK, I was some months past 16, and I came to Communion - the priest was a good Pole, very trad exc Novus Ordo - a few months before 20.

A man with his convictions is a minor calamity if "bishop" of Lutherans or Anglicans, a somewhat heavier one if priest or bishop in an area where he can block or harrass converts who are serious about leaving Reformation, but a disaster of world proportions if accepted by many as Pope.

I wouldn't call him a Lutheran, the position you mentioned is shared by more or less all of the Porvoo Communion - Lutherans, Anglicans, Methodists - I would call him a Porvoo Communion Modernist.

Note, the joint declaration was one of the reasons I went trad - or traddier than before.

And I fear he is the kind of man to whom documents such as "joint declaration of justification" (where Ratzinger was involved, for those preferring to see Ratzinger as Pope) constitute magisterium. Condemnations of Trent were an act of diplomacy, joint declaration is an act of diplomacy, neither is dogma, but both are for their times obliging discipline - that would be his feelings about such things.

It is not for nothing that I left Sweden for a country where more traddy Catholic parishes can be found.

He seems very close to the very humanist but also too modernist Nathan Söderblom.