What examples can you find in Lincoln's address of organizing ideas into groups of three?

I'll assume you mean Lincoln's famous Gettysburg Address.

From that address, here are some examples of organizing ideas in groups of three:

The main example is the overall 3-part outline of ideas in the speech.

Idea 1 (paragraph 1) : This nation was based on the idea that all men are created equal. Idea 2 (paragraph 2) : The Civil War was putting to the test whether or not a nation based on liberty and equality could endure. Dedicating the Gettysburg National Cemetery at the site is a fitting as testimony to the importance of such a nation. Idea 3 (paragraph 3) : We now must dedicate ourselves to continuing the fight for the nation, so "that these dead shall not have died in vain - - that this nation, under God, shall have a new birth of freedom - - and that government of the people, by the people, for the people, shall not perish from the earth."

Another example of three-part statement of an idea comes in the third and final paragraph of the speech. Lincoln said, "In a larger sense, we can not dedicate - - we can not consecrate - - we can not hallow - - this ground. The brave men, living and dead, who struggled here, have consecrated it, far above our poor power to add or detract." Notice how Lincoln uses three phrases to emphasize the idea that any words spoken were not the true honor of this place, but the valor of the men who gave their lives there that had already hallowed the ground at Gettysburg.