I haven't a clue if you have the money to buy the car or not - your age doesn't determine your wealth - so assuming that buying the car is not a problem, it will be the insurance and maintenance costs that will be the biggest burden.
Some supercars require maintenance every so many 1000s of miles and the costs are not cheap when they do. Then you have wear and tear, tyres, brakes etc. But by far the biggest outlay will be your insurance - I would imagine you'll need a suit of coverage for the car, the people, 3rd parties, all sorts of things. There is also likely to be a limit on drivers under 25 or 30. Over a certain mileage your car with dive in value so you'll have a diminishing asset that is expensive to run.
If somebody takes it off the road (which many do because they have no idea how to drive a powerful car - plenty of examples of people crashing expensive hire cars) then you are left without an income whilst the insurance company decide weather to pay out or not. Then there's the speeding tickets, parking fines, congestion charges, minor scuffs and bumps... it will all add up and could become a real headache.
Having said all of that, if you have the money and time (and route to finding customers who are prepared to spend silly money for a few hours in a nice car, and you probably will) then give it a go. If you want an alternative, why not a car club? If you live near any of the large football clubs for example, why not trial a car club idea with some fancy car and see what the uptake is?
My conclusion however is that if you have the money to by a Lambo/Ferrari etc in the first place, you are probably not going to be bothered or worried about faffing around with rentals and wannabe racers. Complete your research before laying out a load of money and an expensive toy!