I found a baby lizard i believe outside in the cold weather and brought him inside where its warmer will the lizard survive?

First, you should identify the species of lizard, and if possible return it to the habitat you found it in. If this is not possible (ie, temperatures have fallen below freezing), then you will need to acquire a cage appropriate for the size of the lizard. Research the heating and lighting requirements. Many lizards require UVB lighting, and they must have thermostat-controlled heat provided for them. The setup for a reptile can be expensive.

Once you have provided a cage with proper heat and light, a small shallow water dish, a hide box, climbing branches if the reptile is arboreal, and appropriate food (most lizards are insectivores--buy crickets at a pet store and coat them with calcium powder before feeding them), you should schedule a vet appointment.

Unless you plan to release the lizard in spring, it will require a vet checkup and fecal exam for parasites. Wild lizards all carry internal parasites, and these can quickly build to lethal levels in captivity, and must be treated promptly. If you plan to release the lizard, then use newspaper to line the cage and change it daily. Sterilize the cage each week.

Mist with water, or provide a humid-hide (directions can be found online) to provide proper humidity for the species of lizard.

If all of the above sounds like too much work, or is too expensive, take the lizard to a wildlife rehabilitator. Do not keep it a day longer than necessary to contact the wildlife rehabber, because the longer it is kept in inappropriate conditions, the more likely it is that the lizard will succumb to stress, develop and infection, and die.