Abraham Lincoln stated that he would endorse the Corwin amendment as a way of saving the Union, by preventing the southern state who had not already let the Union from leaving.
His thoughts at the time:
In a famous 1862 letter to Horace Greeley, Lincoln explained the reasons for his action and his long-held feelings on enslavement and equality:
“My paramount object in this struggle is to save the Union, and is not either to save or to destroy slavery. If I could save the Union without freeing any slave I would do it, and if I could save it by freeing all the slaves I would do it; and if I could save it by freeing some and leaving others alone I would also do that. What I do about slavery, and the colored race, I do because I believe it helps to save the Union; and what I forbear, I forbear because I do not believe it would help to save the Union. I shall do less whenever I shall believe what I am doing hurts the cause, and I shall do more whenever I shall believe doing more will help the cause. I shall try to correct errors when shown to be errors; and I shall adopt new views so fast as they shall appear to be true views.
“I have here stated my purpose according to my view of official duty; and I intend no modification of my oft-expressed personal wish that all men everywhere could be free.”
Source:
https://www.thoughtco.com/corwin-amendment-slavery-and-lincoln-4160928
You may not be aware of this, but Lincoln wrote to the governors of the seceded states as well. He was trying to induce them back into the Union. The South produced 65 million dollars per year of his budget, which is the bulk of it, and he wanted that money to continue coming in.
Lincoln's official position was that states never left the Union, and were in fact just "rebel" states denying the rightful authority of the Federal government.
But Lincoln was a canny bastard, and it is quite probable he was working multiple strategies with his advocacy for the permanent slavery amendment. He often said that if he lost Kentucky, he lost everything.
Keeping Kentucky from going over to the South was likely a significant focus for his actions, and the Corwin Amendment would have mollified them somewhat.
Later he just used force, and after that, it didn't matter what the people of Kentucky wanted, they no longer had the ability to stop him.