The joke American Republicans are telling is that if Abraham Lincoln were alive today, he would vote for Trump. But since he's dead, he will most likely be voting for Hillary.
But how would Lincoln vote if he were alive today?
I understand why people, including Republicans, say it's wrong that the party of Lincoln should nominate Donald Trump. He is of course less a Republican than a sort-of Democrat. However, Donald Trump's promise to deport illegal immigrants would be unlikely to deter Lincoln from voting for his party. Abe, after deciding to free the slaves, originally wanted to send all the freed slaves to Central America.
It is not clear whether he had in mind deporting them. He hoped they would leave voluntarily.
In 1862, Lincoln invited a delegation of black men to the White House, the first time African Americans had been invited to the White House, to suggest this. He told them:
"Your race are suffering, in my judgment, the greatest wrong inflicted on any people. But even when you cease to be slaves, you are cut off from many of the advantages which the other race enjoys. The aspiration of man is to enjoy equality with the best when free; but on this broad continent not a single man of your race is made the equal of a single man of ours.
...It is better for us both, therefore, to be separated. There is an unwillingness on the part of our people, harsh as it may be, for you free coloured people to remain...." Continued here.