Actually, you have a good point there. In all the SFB Manuals I got, I don't recall anything saying that the Social Structure of the Lyrans was "Matriarcal". I thought the SFB Manuals indicated that the Seletolians had this kind of structure (i think?), but I'm not sure on this. I thought the Lyrans had pretty much a Feudalistic Government that was more or less organized then the Kzinti's (less Cival Wars then what the Kzintis went through).
Might just be a SFC add in when SFC1 was first made.