1602 58th Street 1602 58th St, Lubbock, TX is a rental apartment building with 2 floorplans available. It is located in the Bayless Atkins neighborhood of Lubbock. It has apartment amenities including in-unit laundry, air conditioning, and dishwasher. It has building amenities including outdoor space, and garage parking. Cats and dogs are allowed, making it a pet-friendly building.