Does the lemon law apply to cars bought with a service contract only?

No. The California Supreme Court recently ruled that service contracts (also known as extended warranties) are not covered by the lemon law. Service contracts are promises to repair. If a service contract refuses coverage without a good reason, you may sue the service contract company (and possibly the dealer that sold it to you) for the cost of repair.  more

Yes. As of 1998, the California Court of Appeals ruled that a service contract gives a consumer lemon law rights. If a consumer buys a car with a service contract, there is at the very least an implied warranty for up to a year’s time after purchase. A purchase with a service contract cannot be an "as-is" purchase. The consumer would have lemon law rights against the selling dealer and also the service contract provider.  more