Being under anesthesia can be a long and expensive process that can also present several unwanted complications. Because of the short duration of LASIK and its relative safety, general anesthesia is not required, as it will only increase the cost and require more recovery time. This is why you won't need general anesthesia. Being “lying down” has its own risks and would mostly only increase the cost of surgery.
General anesthesia during LASIK surgery doesn't provide much benefit, which is why the vast majority of patients stay awake during short surgery. There's really no need for general anesthesia in laser vision correction procedures. In fact, you need to be awake and able to cooperate to get the best results. Fortunately, with oral Valium and highly effective anesthetic eye drops, this isn't as difficult or as scary as you might think.
No, the surgeon won't put you to sleep because he needs you to be alert throughout the process to provide information about how your eye feels.