Can a leopard gecko live without a heating pad but with just a light?

Leopard geckos should be given a temperature gradient of 80F with a 90F hot spot during the day, and can drop to 70F with an 80F hot spot at night. So, unless your house is 80F at night, the answer is no. Nor should you ever use a heat pad, cord, or heat tape without a reliable thermostat to connect it to. Proper equipment will keep your animal safe and healthy. Leopard geckos may live for over 30 years with proper care--$120 for proper heating equipment and thermostat is not exactly a huge expense for the life of your animal. If you cannot afford it, don't get a leopard gecko.