Get reviews, hours, directions, coupons and more for Western Bank. Search for other Commercial & Savings Banks on The Real Yellow Pages®. Western Bank (Lordsburg, NM) Locations in Your Area. Western Bank (Lordsburg, NM) has 5 branches in their local area. This traditional brick and mortar bank. Relationships with our customers are important to us. Hear directly from them what it's like to partner with Western Bank! Learn More.