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Sounds like every single episode of House.
The two most relevant tropes there would seem to be:
Dark Secret — They're usually lying to cover up something embarrassing, like an unusual international trip, or that their company is not prestigious, or that they're breaking their religion's rules, or that they have an off-the-books job.
Idiot Ball — The fact that they could have a potentially fatal illness and yet are putting petty dignity above their own health, that they'd rather die than admit to a doctor that they own a junkyard.
Dark Secret covers the secret itself, not the fact that the lie prevents proper diagnosis. And the lies usually are disconnected enough from the symptoms that I can't call it Idiot Ball, although there are a few exceptions.
Shameful Source of Knowledge? In that they know what they did wrong but are ashamed of the truth.

A patient, or a member of his/her family, lies to some degree about the patient's background, believing this lie has nothing to do with the patient's diagnosis and treatment. However, it turns out to be a key to the correct diagnosis. Examples include:
- The patient's father claims that he never left the US. Turns out he left to a third-world country and picked up a disease which never got diagnosed in him, but he transferred it to his son.
- A father claims to own a construction company. Turns out he actually owns a junk yard, and the son got sick from a key chain made from material in that junk yard which turned out to be radioactive.
- A patient claims to be Jewish (Jews, including secular ones, don't eat pork; although this generalization is not as guaranteed as the episode in question implies), but got sick from eating improperly prepared pork.
- A patient claims that he doesn’t work on Saturday, but it turns out that the primary disease he has is from an infection caused by handling dead birds at his Saturday job.
Edited by Someone1981