In Star Wars: Attacks of the Clones, why did Dooku tell Obi-wan about the Senate being under the control of a Sith Lord? Was it because Dooku had a back-stab plan for Sidious or just because Sidious had wanted him to do it?
Dooku is actually playing a pretty clever game here. It would definitely serve the Sith's plans of Galactic domination if they can get a member of the Jedi Council to join them and he knows that the Jedi, and Obi-Wan in particular, have been harbouring serious doubts about the motives of Palpatine and the Senate.
By offering a captive Obi-Wan some important-sounding (but ultimately worthless) information about Sidious' secret name and and a half-truth that the Senate is under the influence of the Sith, he hopes to convince Obi-Wan that despite their violent ways, the Separatists are actually on the side of the angels in this conflict, valiantly fighting against a Sith-inspired Senate plot to destroy their freedom. Unfortunately (for Dooku), Obi-Wan overheard his battle plans a few minutes before and is not fooled by Dooku's lies.