Assuming the photo is fairly representative of the entire firebox, what's it going to take to repair all of the mortar joints in terms of time/cost? The width at the back is 24, the front is 30, and the height of the area needing repair is 30.
When dry skin is the cause of an itching back, it is easily remedied by applying a lotion or cream to moisturize the area. When chronic dryness and itchiness is an issue, a person may need to increase hydration efforts.
The most obvious cause of burning in the lower back is an actual burn on your skin. This could be from a sunburn, a substance such as IcyHot, or burning from a heat source, such as a heating pad. You can determine if this is the cause of your pain if it is localized to your skin.