The Lyran Senate was an executive body of the Lyran Star Empire, tasked with the day-to-day administration of the Empire. However, it has almost no legislative power. (TOS video game: Starfleet Command (game))
Each Lyran count and Lyran duke appointed one senator apiece, with the King-Emperor of the Lyran Star Empire also appointing a senator. (Star Trek: The Stoneship Files: "Educational Armageddon")
Background
The Senate has been mentioned only once in SFC1 in a pre-mission briefing of the main Lyran storyline (both Red Claw and Iron Fang).