Even if all that is true (I have my doubts) that wouldn't make Lula a fascist.
Lula’s party has a history of totalitarian tendencies and of siding with dictatorships (Cuba, Venezuela, Libya, Angola, etc) and a well known desire to control the media (of course, they call it “democratizing the media”).
If dictatorships, totalitarianism and state-sponsored censorship are not fascist, I don’t know what is.
A few more key characteristics of fascism: nationalism, overt anti-egalitarianism, militarism.
Bolsonero is the fascist here. Lula is not.
Bolsonaro tried to reduce the size of the state, in direct contradiction with that.
Please list concrete actions by his government that can be reasonably characterized as “anti-egalitarian” or “militaristic”.
In fact the military in his government was mostly used in the process of helping Venezuelan refugees escape their country into Brazil.
Mussolini and Hitler did not care about empowering "the State" for its own sake. The State was simply a vehicle to exercise a particular racial and/or political ideology and to gain personal power. If they could've excised state apparatuses and achieved power in some other way, they would've. Indeed, that's exactly what both dictators (though more so Hitler) did once they found the appropriate political leverage to do so. Everything is subordinate not to the State, but to the Fuhrer. The State itself was subordinate to the Fuhrer. You only need look at Hitler's public actions leading up to the war, not to mention the private memoranda, letters, and other documents, to see that. How many times did Hitler risk the complete destruction or occupation of Germany by the Versailles powers? How many times did he exclaim that if he failed, Germany would fail, and would deserve it? Hitler did not care about the State, he cared about his own personal power and legacy and maintaining the facade at all costs.
Fascists use the state to empower themselves. By reducing its size, by definition, a politician reduces his own sphere of influence.
Rereading your comment, I think you’re more or less equating the State with the country, while I’m talking about the government and supporting structure and bureaucracy.
Of course Hitler didn’t care about Germany. He cared about his own power and he had an overreaching state under his control to maintain it.