Honestly, I think that's a position in the credibility stakes with the claim that the Democrats stole the 2020 US presidential election through mass voter fraud.
The story seems to me more about over-aggressive, ambitious and slightly slipshod prosecutors. They wanted to move quickly, there were legitimate international dimensions to the case, and they could get leverage against suspects through the USA - the cost was exposure to interests from the US side of things. But there's plenty of information from scoops in, for instance, The Intercept showing that the prosecutors were by no means US stooges and aware of protecting Brazilian interests from the USA. We can hardly deny that the dirt on people all around Dilma Rousseff is awkward, even despite her appearing clean herself. Similarly that for the improprieties around Lula's conviction, again those around him were corrupt and his dealings have not been transparent enough for us to be confident about him personally.
Did the USA interfere in ways to potentially advance their own interests? Apparently so. Did they cook it up and trick Brazil just to take down the Brazilian left? Almost certainly not. The latter sounds to me like a comforting narrative for the left to invent to cover for the fact that many of their own were caught and tarnished, doubly attractive for tapping into the perennial fear of US manipulation.
But given that Bolsonaro's family is also seemingly neck-deep in corruption and he's a frothingly disturbing quasi-fascist as well, one can only see Lula as a massive improvement.