I think the "lie" comes from the paradox of what liberalism says it can do and what it actually does. We strive (or we say we strive) for ideals, but we fall short. Then our ideals are degraded.

If one goes to Wikipedia to investigate any ideology like "liberalism" or "socialism," one finds there is a whole whack of subdivisions of these ideologies, and sometimes these subdivisions are not too compatible with each other. Only scholars and people with not much else to do in their lives can make the distinction between these sub-divisions. Yet we like to use the broad terms as if we have a collective understanding of their meaning. But we don't. And yet we keep trying. Maybe that is the lie.