There are several synonyms for the phrase "be based on lies" that can be used to describe falsehoods and deceit. One such synonym is the phrase "built on deception," which suggests that the foundation of the claim is false or fraudulent. Another option is "founded on untruths," which indicates that the basis of the assertion is not rooted in reality or fact. Similarly, "stemming from falsehoods" emphasizes that the source of the claim is an untruth or fabrication. Finally, "grounded in lies" implies that the statement or belief is firmly anchored in falsehoods, making it difficult to disprove or dispel.