What was the theme of the lincoln-Douglas debates?

Answer 1

If you mean the actual debates between Abraham Lincoln and Stephen A. Douglas...

--It was mostly the topic of slavery and the will of the negro

--The Lincoln-Douglas debates of 1858 where a series of debates around the State of Illinois. Each man was his party's candidate for the US Senate from Illinois. At that time, there was no direct election of Senators, rather they where picked by the state legislature.

The debate focused on issues of the day. However, a major issue of the day was the expansion of slavery into the territories, which in time would become states. A variety of opinions, both pragmatic and idealistic prevailed among people of good will. However it was a very "hot" topic, and during the debate each man framed the talking points that where to take even more center stage in the next campaign between the two: the Presidential campaign of 1860.

If you mean, instead, the debate style today known as "Lincoln-Douglas", it's a values-oriented debate (with the central question coming down to "Is X good/right?") as opposed to the more policy-oriented CX-style debates (where the negative team can acknowledge that the current situation is not ideal and still win by showing that the affirmative team's plan is either unworkable or worse than doing nothing).