What is the downside of the police lying? Assuming they didn't have a warrant then they either lie and it doesn't make the situation worse as police are allowed to lie or they don't lie and guarantee a lawsuit.

I'd understand the argument for why they're incentivized to get a warrant in the first place (even assuming parallel construction is a viable alternative to getting a warrant as they may be caught) but that doesn't mean they wouldn't lie after they got caught screwing up.