You can do this.
I am sorry that most of the responses so far have been dismissive. I think that some may have considered the task too big for them to accomplish and therefor doubted your ability to do the task.
As you will have gathered from some of the answers, you cannot just take the code and transfer it to your phone and make it run with the aid of a few tools, such as an emulator. At least, as far as I know, there are no emulators that run under iOS which will emulate Microsoft Windows, Gameboy, PlayStation, or Nintendo 64, the platforms that Lego Racers was developed to run under.
The task then is to write a "copy" of the game that will run under iOS. There are copyright issues, but as long as you are not planning on publicly distributing the results, or exhibiting the results in a public place, you probably won't break any laws or open yourself to legal action.
Your question indicates that you are not afraid of programming. The main programming language for iOS is Objective-C. The Apple website offers an integrated development environment (IDE) that will make the programming experience much easier, called
Xcode. Most seasoned programmers use an IDE, and there are sometimes arguements about which is the best, but this one from Apple, as you want to target an Apple device, is probably going to be the best one for a beginner.
There are alternatives which promise to be easier, although they come with a price-tag. These are game creation platforms, most of which don’t require any programming knowledge. You may have to sacrifice some flexibility, but if you don’t have the time to learn a programming language then this is an option. Check out the websites for
GameSalad,
GameMaker: Studio,
Stencyl, and
Construct.
Whichever option you choose, if you stick with it you will learn some valuable skills. As you probably already know, the ability to take an idea. no matter that it's not your own, and make a working game out of it, offers many employment oppertunities. Even if you don't want to work in the games field, being able to show that you chose a project and that you stuck with it until completion will go down very well at any job interview.
I have been a programmer for many years, and I have made a good living out of turning others peoples ideas into reality, or refining others working constructs into a polished and robust app that is suitable for public use. I first learnt how to program by setting out to do something similar (mobile phones didn't exist back then). Give it a shot and see where it takes you.