Dante the politician
I dunno 'bout Dante-as-Lenin. He was a believer in Imperial authority in Italy (at least insofar as it diminished the secular power of the Papacy), and I don't think he had any real populist leanings. I have to stress that in the course of this thought experiment, I want Dante to remain recognizable as himself...I don't remember if he wrote his political treatise (
Monarchia) before, during, or after the
Comedy. The thing that intrigues me about him is that he did have a degree of power as a prior of Florence (a sort of city councilman), and if he had parleyed that into something more, he could pretty much have butterflied away a good deal of the Renaissance and subsequent history.
Other ideas - if Italy north of the Papal States could be unified (either alone or under Henry VII-the HREmperor in whom Dante reposed the most hope in his time of exile) such a state could strong-arm Venice into financing a Tenth Crusade - it doesn't have to take Jerusalem, just piss away Europe's finances and energy just as its getting ready to start exploring (gaining Jerusalem only to lose America). Genoa, fr'instance, would be part of such a state.
-Maybe have all-out warfare between our Dante-based Tuscan superstate and the Papacy, leading to monarchs all over Europe taking charge of their national churches a la Henry the VIII of England. Or alternately, for a three-sided European war between the French, the Germans and Italians, and the Pope). And peace coming just in time for the arrival of the Black Death.
-The Medicis might never rise to prominence, so not so much art or architecture, at least outside of the Vatican. Leonardo da Vinci has to keep his day job.

Or instead of
David he has to build a Herculean sculpture of
Dante, the Great Dictator in the Piazza della Signoria.
-I can picture life in a state ruled or strongly influenced by Dante as being very scary (requiring absolute secular obedience to the state and absolute religious obedience to the church).
-I'm not sure all of this could possibly take place within the space of one lifetime (Dante was exiled in 1301 and died 20 years later-maybe add five years or so given that he won't suffer the discomforts of having to move around a lot).