Can I continue to drive the vehicle while making a lemon law claim?
If you make a lemon law claim on a vehicle because you believe it is defective and the warranty has been violated, you are not prevented from continuing to drive the "lemon" vehicle in the meantime. The vehicle is still your property, and because the case revolves around a defect caused by the manufacturer, it's very unlikely that anything that might occur based upon the lemon car's use could affect the case in a negative way. In other words, unless driving the vehicle might make the problem disappear, you probably don't have to worry about driving it while making a lemon law claim.
Of course, while lemon law for cars doesn't prevent you from driving the vehicle, in many cases a defect will make the vehicle unsafe to drive, and in these cases, stop driving it. Don't make the mistake of thinking that if something goes wrong the manufacturer will also be held responsible for costs of an accident or repairs caused by the unsafe state of the car. If you know it's unsafe and continue to drive it, you will be liable for any accidents. This is something lemon law does not protect against.
Finally, under lemon law, it's important to remember one thing: should your case result in the manufacturer taking the vehicle back into their possession and compensating you for it, the condition of the lemon vehicle will be taken into consideration. The vehicle will be examined for any damage beyond typical wear and tear, and that damage may be deducted from your settlement. Thus, technically continuing to drive the lemon car could open you up to having something happen that would reduce its value. But the odds of that, versus your potential need for the car in the meantime, are up to you to calculate.
If you are making a lemon law claim, you should have a lawyer on your side. A consumer or lemon law attorney can answer any questions and provide you with answers appropriate for your state's lemon laws, so you can make sure you don't do anything to jeopardize your legal right to recover damages.