Depending on the rarity and/or criticality of your medical issue, my guess would be sooner for more complex issue; but I cant say that for sure. Mayo doesn't accept everyone who applies to be a patient. The triage team that reviewed my request took 2- 1/2 days to review my request whether to be seen by them, and my 1st appt was within 10 days.
I don't have lung cancer, and all insurances have different allowances for the same surgeries, so I don't have any idea what your costs would be. I can say that the amounts charged to my insurances for all the plethora of tests and procedures Ive had done seem to be roughly in the same amounts as what it costs at home, like CT & MRI cans, blood draws, anesthesia, hospital daily costs, office visits. Medical care is EXPENSIVE, for sure!
Best wishes to you with your care.