Lincoln started his political career as a Whig, so it is only appropriate that he turned into a Whig historian. His reinterpretation of American history in the Gettysburg Address as a narrative of ever increasing equality, inclusion, and freedom is pure Whig history. It has also been enormously influential, most notably in the speeches of MLK and Barack Obama. The objections in the 1619 Project notwithstanding, it is still the prevailing opinion in America today.
But is it true? The historical evidence is mixed. If you look at purely economic issues, you can hardly argue that increased equality has been a hallmark of American history. What you find is the following: a period of relative equality, due to the ready availability of land, for white people (not slaves, obviously) prior to the Civil War; the temporary crushing of the plantation economy and the freeing of the slaves during the war; the failure of Reconstruction and the rise of enormous corporations and plutocrats in the late 19th century; some slight mitigation of inequality as a result of reforms in the early 20th century; a period of massively increased equality arising from the Great Depression and World War II; and a long era of increased inequality after 1980, due to the victory of GOP supply side economics. The evidence is more consistent with Piketty than the Whigs.
The political part of the story is a bit more encouraging. Here, you see relative stability (minus the slavery issue, of course) up to the Civil War; the massive, mostly unanticipated experiment of Reconstruction; the ultimate termination of black inclusion during Reconstruction; expansions of popular voting rights during the early 20th century; and the victories of the Civil Rights Movement in the 1960s. Today, however, the GOP is trying to turn back the clock and limit voting to its constituents, without admitting that it is doing any such thing. It is not foreordained that these efforts will fail; in fact, they will probably become more pervasive, under the bogus rationale of “fraud,” as the result of the 2020 election.
So, on balance, was Lincoln right? In the economic sphere, no. In the political sphere, broadly, yes, but the gains cannot be taken for granted, and are under attack even today.