Ask Mr. Smarty Plants

Since you say it isn't Salvia azurea (Pitcher sage) (USDA Plants Database distribution map shows it occurring in adjacent Lamb County although not in Lubbock County) or Scutellaria resinosa (Resin-dot skullcap) ( USDA Plants Database distribution map shows it occurring in Lubbock County), Mr. Smarty Plants is left with only a few choices that are native and in the Family Lamiaceae (mint family) with flowers that would resemble Salvia azurea.  (You will note that I interpreted "blue" rather broadly, including "purple" and "violet" in my search terms as well).  They are:

• Hedeoma drummondii (Drummond's false pennyroyal)  USDA Plants Database distribution map shows it occurring in Lubbock County.  Here are more photos and information from Southwest Colorado Wildflowers.

• Salvia reflexa (Lanceleaf sage)  USDA Plants Database distribution map shows it occurring in Lubbock County.

There are three native species of Monarda that occur in Lubbock County, although I don't think they really fit your description.  They are

Monarda pectinata (Pony beebalm)

Monarda citriodora (Lemon beebalm)

Monarda clinopodioides (Basil beebalm)

There is one other possibility in the mint family, Lamium amplexicaule (Henbit), an introduced non-native species, that is shown occurring in Lubbock County on the USDA Plants Database distribution map.  Here are more photos of henbit from Identify That Plant.

Here are a few possibilities from the Family Scrophulariaceae (Figwort Family) that has flowers that are similar in structure to the mint family flowers.

Nuttallanthus texanus (Texas toad-flax)  The USDA Plants Database distribution map shows it occurring in Lubbock County.  it normally blooms February through May.

Penstemon buckleyi (Buckley's penstemon) blooms in April-May.  The USDA Plants Database distribution map shows it occurring in Lubbock County.

Penstemon fendleri (Fendler's penstemon) blooms April through July.  The USDA Plants Database distribution map shows it occurring in Lubbock County.

If none of the above is the plant you saw in bloom in September and you have a photograph or photographs, please visit our Plant Identification page to find links to several plant identification forums that will accept photos of plants for identification.  You might also consider contacting someone in the South Plains Lubbock Chapter of the Native Plant Society of Texas to see if they can help you identify the plant.