You're using "lawful warrant" wrong.

You say it was not a lawful warrant... But it was lawfully issued by a judge upon finding of probable cause.

The fact that it was predicated on false information does not mean that the warrant was "not lawful" in the sense that the judge made a finding of sufficient probable cause based on the information he or she was presented with.

You are essentially asserting that a facially valid warrant issued by a judge cannot be relied upon on its own and thus every single officer on scene is responsible for personally verifying the information relied upon for the warrant.

This is a complete non-starter. The police have to be able to rely on these warrants. Whether the police are lawfully allowed to enter and whether evidence gathered will be admissible in the underlying case are two separate issues.