Interesting way to look at it. The new Republican Party of Lincoln’s time was not conservative. One of its founders, Horace Greeley, published Karl Marx for years in his New York Tribune, the leading newspaper of its time (like the later NY Times was until recently).
Liberal big City Corporate Lawyer who was in the thrall of Plutocrat industrialists and who loved to tax, borrow and spend, and greatly expanded the power and scope of government?
Yeah, Lincoln was very much a Liberal for his era.
If you look at the dividing line as Urban versus Rural, or Hamiltonians versus Jeffersonians, it becomes clear which side is always liberal and which side is always conservative.