Kathrine intentionally wrapped herself in the lyran elements though, as a way to cultivate connections to the Lyran half of the realm when the lyran portion started seeing unrest after the clan invasion. she saw a path to power and took it, intentionally playing up her lyran heritage over her davion. (to the point of adopting her grandmother's name)
Victor on the otherhand got viewed as a "davion" largely because Kathrine adopted a lyran persona.. since Victor was in charge, and the Lyrans were getting more fed up with the davion half (which hadn't been hurt directly by the clan invasion), anyone supporting the Status Quo would inevitably end up viewed as "anti-lyran." since Victor wasn't going to elevate the lyran half above the whole of the decom, yet he wasn't pro-kurita, marik, or Liao, "davion" became the label of choice. something kathrine encouraged after the split.
her manuevering bit her in the ass though after she finally got the throne of the fedsuns half as well.. the way she'd built herself up as a "lyran princess" and tried to use that power base to control both sides of the fedcom alienated the fedsuns populace, and her fixation with being in control of the fedsuns side also started alienating her lyran supporters.
honestly the way she went about getting control, the fedcom civil war was inevitable.