A Household has no truce to offer a flood, and none to seek. The Imperial Knights stand in permanent enmity with the swarms and tides that out-body a lance — the Ork mobs, the Tyranid broods, the Genestealer Cults, the massed Guard blobs — the natural predators of a gang two to four models strong.
There is no alliance to be made here and no shared banner: the tide exists to drown the giants, and the giants exist to hold against the tide. In campaign play, a swarm House sharing a world with the Knights seizes the initiative in scenarios fought against them, flooding activations the lance can never match. This enmity stands throughout the campaign — it is never bought off, and the Household never seeks to.