The answer to your question would be that the definition that explains best the effect of the selected phrase is the following one: It suggests a much-deserved justice.
This phrase is part of Lincoln's second inaugural address in which he argues an end to the War. He wishes for the nation to be a whole once again. The fact is that Lincoln believed that the war had been sent by God to the US as punishment for slavery, so he claimed that it wouldn't end until all the suffering of the slaves had been dealt out to soldiers ("until every drop of blood drawn with the lash shall be paid by another drawn with the sword").