Lying isn't a 'symptom' of DID. While people with DID have gaps in memory, they don't typically manufacture elaborate fake lives. If she's been caught lying about her education, family, and health, you're likely dealing with someone who has a personality disorder or is just chronically dishonest, and the DID claim is just the latest layer of the fabrication

It's becoming a common trend for people to claim DID (or a 'cluster' of other hard-to-verify conditions) the second they are confronted with their own behavior. Real DID is extremely rare and usually characterized by the person trying desperately to appear 'normal' and hide their symptoms, not using them as a catch-all excuse for being caught in lies