All perfect praise be to Allah, The Lord of the Worlds, and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
According to the Shafie school, if a small part of a person`s Awrah (Parts of the body that must be concealed during prayer) was uncovered during prayer, prayer is invalidated unless the praying person covers that part immediately, but there is disagreement among scholars in this regard.
Therefore, prayer should be re-performed if the praying person realized that part of his/her Awrah was uncovered during it.
Al-Imam An-Nawawi (May Allah be pleased with him) said: "Covering one`s Awrah is a condition for the validity of prayer. Therefore, if part of it was uncovered then prayer is invalid, whether that part was small or big-even the smallest part-the praying person was man or woman, prayer was before people or in isolation, voluntary or obligatory prayer, and whether it was funeral, Tawaf, or Sujud-at-Tilawah prayer." {Al-Majmou`, vol.3/pp.172}.
Accordingly, if a person`s lower back, what`s lower than the level of the navel, was uncovered then prayer is invalid and should be re-performed, according to the Shafie school of thought. In fact, it is the duty of every Muslim to wear clothes that cover the Awrah and are suitable for prayer which one offers for the sake of Allah, The Almighty.
Nonetheless, we shouldn`t judge others prayer as invalid because part of their Awrah was uncovered since there is disagreement among scholars in this regard, and every Muslim should do their best to be on the safe side as far as performing acts of worship is concerned. And Allah Knows Best.