Design your own Lamborghini Game
Yes. Their names, logos, and body designs are all trademarked and cannot be used in any capacity outside those explicitly allowed by trademark law, which almost certainly excluded use in your game. And expect to be completely incapable of acquiring those licenses for reasonable terms, as the licenses are generally very expensive and come with a mile long list of stipulations.
Even though you'll be paying them, the companies will be seeing your game as another advertisement for their cars. They will completely reject working with you unless they believe your game will make their cars look awesome and make your players want to buy them.
There was a "car czar" for the Forza 4 team. His full time job was to make sure their car models and car performance matched the various licensing agreements they had, to make sure the cars were modeled accurately, and so on. You need a full time guy just to do that if you want to license cars. And expect weird incompatible licensing terms to happen and look forward to wasting tons of time resolving them. E.g., two manufacturers who want their car to be the fastest car in your game, or who refuse to allow one player selectable color to be applies to their car, or to refuse to allow damage to apply to their car, or to demand that the car can only be used if you model every little mechanical detail to a level of accuracy that your artists or your engine possivly can't handle.
As with all things in the small game and indie space, you are far better off being original and unique.
Also remember that if you try to make games that have the same selling points as AAA titles (like having real cars like Forza does), your game is going to get compared to those games, and is highly unlikely to come out with high marks. Strive to be unique so your game can stand in its own rather than be compared to games with tens of millions of dollars put into them.