CT can be seen on xray, but not always. Fluoroscopy would be needed if you wanted a more definitive answer. That wouldn't be something you'd do with an asymptomatic dog though. I don't know of any genetic testing for it.
LP, as YorkieRose said, doesn't require xrays to diagnose. They can try to grade the disease this way, but vets can tell by palpation whether or not it is present.
LCP - not so sure. I'd think an xray would show it, but don't know of genetic testing for it. It's not nearly as common as LP. I wouldn't worry about it unelss you are noting hips issues in your pup.
Because different contrasts are required for different parts of the body, it is doubtful that a vet could get a good look at the trachea and hips at the same time. I wouldn't be too anxious to look into any of this unless you are seeing symptoms (or unless you are breeding of course).
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