“voluntary”. Riiiight.
What a joke. Blacks were also to be “encouraged” to “voluntarily” leave Northern states by the Black Codes they adopted which denied Blacks all civil rights, set huge bonds as a requirement for them to move there, prevented them from being able to enforce contracts or testify against Whites in court, etc etc. That was the sense in which deportation would be “voluntary”.
The pre-Civil War Black Codes did indeed restrict the rights of African Americans in some Northern states. They were not always strictly enforced. Most of those laws were repealed in the mid-19th century, before or after the Civil War. The fifteenth amendment ended voting restrictions in the North and what remained was laws against interracial marriage. That's not to say that discrimination ended, just that the situation you described didn't exactly apply after the Civil War.
In the South after the Civil War restrictive Black Codes were being introduced to replace the old Slave Codes that had controlled African-Americans and restricted their rights. It's hard to see what Lincoln may have had to do with Southern states imposing segregation and Black Codes. I'd say that the very fact that Black leaders were free to come to the White House and discuss the plan with Lincoln suggests that conditions in the North weren't as oppressive as you claimed and that Lincoln wasn't committed to forcible relocation either.