Lincoln was most certainly a Liberal within the context of nineteenth century politics, much like every American politician of his day that didn't own slaves/sympathise with those that did.
Hamilton didn't own slaves, and I think today he is consistently considered a conservative.
But i'd consider Lincoln a Liberal because he pushed for nationalization of the railroads, created the first income tax, was against free trade (but I suppose back than conservatism was against that in general.) and generally meddled in the affairs of the economy, ex. the Homestead Act. Not to mention his suspension of Habeas Corpus, and invading the south.