As a politician of his times in the 1850s, Lincoln's expressed views were not dissimilar from those of other "moderate" Republicans -- he did not believe in abolishing slavery in the South, but did want it restricted from the western territories, and absolutely disagreed with interpretations of the Supreme Court's 1857 Dred Scott decision which suggested the Constitution required slavery to be lawful in every state!
As to whether Lincoln considered our Declaration of Independence the source-authority for abolitionism, I'd much doubt that.
The reason is that most ardent abolitionists took their beliefs directly from their understandings of the Bible's views on slavery, beginning with God's leading the Israelites out of Egypt.
Is that clear enough for you?
It was never unclear, but you underestimate the influence of the Declaration of Independence. The freedom cases filed in Massachusetts and which ended slavery in that state were based on interpreting the Declaration as covering "all men" including slaves.
Even back then Liberal Massachusetts was leading the nation in re-interpreting the law based on their own preferred beliefs rather than actual original intent.
That exact same tactic was tried in Pennsylvania by William Rawle and a consortium of other attorneys, and it was voted down unanimously by the then Supreme court of Pennsylvania.
The reason I know about this is because after going down to a crushing defeat in Pennsylvania, William Rawle tried the tactic of arguing that English Common law was the basis for citizenship in the United States and that it therefore made slaves born here into free men. It didn't go anywhere while he was alive, but his famous legal book "A View of the Constitution" managed to spread the idea all across the nation, and I blame the influence of this book in no small part to the subsequent belief that our citizenship was based on English common law, rather than the natural law as expressed in the document which created US Citizenship, the Declaration of Independence.
Much mischief has been the result of this deliberate misleading, and I say deliberate because Rawle very well knew and had been informed by pretty much the entire legal community of Pennsylvania that our citizenship was based on natural law as outlined by Vattel, and not English common law. Rawle had an agenda to abolish slavery, and this was but one more vehicle he attempted to use to accomplish that task.
It didn't work, but it certainly caused a lot of other problems later.