Learn how Peoples Bank (Lubbock, TX) is rated and compare its account fees, customer reviews, and latest bank accounts interest rates. Find out if it's worth. Download Peoples Bank Texas Mobile and enjoy it on your iPhone, iPad, and iPod touch. Peoples Bank Texas Mobile 4+ Lubbock National Bank Mobile. Peoples Bank. Lubbock, TX. Contact Info. Andy Turner. President. Address: 34th St. Lubbock, TX Phone: () Find us on: Formed.