A novel sorghum variety designated PHLQVZQ and seed, plants, plant parts and plant cells thereof are produced from a cross of inbred sorghum varieties. Methods for producing a sorghum plant by crossing hybrid sorghum variety PHLQVZQ with another sorghum plant and methods for producing a sorghum plant containing in its genetic material one or more traits introgressed into PHLQVZQ through backcross conversion and/or transformation, and to the sorghum seed, plant and plant part produced thereby are described. Sorghum variety PHLQVZQ, the seed, the plant produced from the seed, and variants, mutants, and minor modifications of sorghum variety PHLQVZQ are provided.