Lincoln did more to preserve, protect and defend the Constitution than anyone of his time, or, arguably, since.
"Even still, the votes they got after aren’t enough to affect that large change. That happened later."
Lincoln did support the 13th Amendment and there's no reason to suggest he would not also have supported the 14th & 15th, had he lived.
Except for Article IV, section 2 when he dictatorially discarded on his own authority. (Among other constitutional laws he ignored or broke.)