Usually factions don’t get solo books. You’ll have to look at the Lyran section of various plot books
House Steiner: The Lyran Commonwealth (3025)
FedCom Civil War (3062-3067)
Era Report: 2750, 3052, 3062, 3145
Field Manual: Updates, 3085, 3145
Jihad Secrets: The Blake Documents (3075)
Jihad: Final Reckoning (3082?)
First and Second Succession War
Depending on how much of a deep dive you want to go on, there are also a few Lyran-centric scenario packs from the Fasa days like Coventry that contain plot information