The Lord had told Lot and his wife to escape to the mountains and not be looking back at the past behind them. Maybe Lots wife did not have faith in the Lords ability to provide a future for her as good as her past and that is why she was longingly looking back. Jesus tells us to remember Lots wife as a warning against trusting our self as the source of life provisions, but by faith be willing to lose our old life for the new life He has provided for us. When we come to Jesus He gives us grace and mercy; grace to bring us into a new powerful life, and mercy as He forgets the mistakes we have made in the past. We are warned that looking back at our past provision or mistakes can cause us loss and rip out of our grasp that for which Christ wants us to have.
Lots wife had a strong attachment to the past which outweighed her confidence in the future and caused her to reject Gods Word. Many people read the old testament laws the same way thinking these past rules apply to the new covenant we live in. Paul tells us we are dead to the law for when Christ died he took that entire rule-dominated way of life down with him and left it in the tomb. (Romans 7:1-6) Paul said He is not looking back at the past, but the one thing he does is forgets the things behind and presses toward the mark of the high calling of Jesus. (Philippians 3:13) To be tied to our mistakes or abilities to provide for ourselves is a manner of looking back that can cause us to miss why the Lord has given us the free gift of Righteousness to get hold of the new future we have in Him.
If we had a bad past we no longer should torture ourselves with these bad memories. If we have suffered loss we can forget the things that are behind and enter into the rest of the Lord waiting to see what He will provide in the future. The past can be learned from, then we look ahead knowing that faith is pointing towards the future. To yearn for the past with a dismal view of the future can be considered looking back same as the sin of Lots wife. Beloved have faith in God that He can provide a future for you that is above and beyond your past, better than you can imagine. Then you will have remembered the mistake of looking back like Lots wife and can lose your old life to preserve the new one.