“Lying is fraud. Fraud is a crime.”
Incorrect.
Fraud means: (1) intentionally lie; (2) with the intent to defraud; (3) trick someone (reliance on the lie) and (4) cause damage by the lie.
If someone is just a faker without intent to get something (e.g., vet benefits, job, etc), then it’s not fraud.
If you lie to someone, you are committing fraud.
Whether or not it is a criminal offense is up to whatever remains of our "justice" system.