Um, no, the first freeing of slaves was as a result of the 1807 Slave Trade Act, after which Royal navy ships regularly freed slaves from ships sailing between Africa and North America. This was further advanced with the 1833 Slavery Abolition Act which freed the existing slaves in the Caribbean and other British colonies.
During the next few decades most other former slave-trading and owning nations followed suit, the United States not finally abandoning it until 1865 at the end of its civil war.
These Acts came about as a result of tireless campaigning by many, but most notably William Wilberforce and Thomas Clarkson.
So neither Lincoln or Johnson would be correct; while they played a part, the freeing had begun some time before.