Does the exposure of part of the lower back during prayer affect its validity, given that it is below the navel and considered 'awrah, especially since the questioner is wearing a summer thobe?

If the garment does not describe the color of the skin, prayer performed in it is valid, even if it describes what is beneath it from other clothing. What is obligatory to cover between the navel and the knee during prayer. If a small part of the 'awrah (private parts) is uncovered unintentionally, it does not matter even if the duration is long. And if what is uncovered is not a small amount, but the worshiper hastens to cover it before a long time passes, it also does not matter. However, if a part of the 'awrah is uncovered and it is considered immodest ('fahish') by custom, and a long time passes, or the uncovering was intentional, then the prayer must be repeated.