Closest area to Lubbock with lift access that I can think of would be Sandia Peak, just East of Albuquerque. The lifts run on the weekend.
Sandia Peak
If you're into more freeride stuff, then closest would be
Pajarito in Los Alamos, or
Angelfire. Los Alamos is probably 2 hours closer to you than Angelfire, but still a good 8 hour drive from Lubbock. Check the Pajarito schedule before going...they're open every other weekend.
If you want something closer and are willing to pedal to the top, then the mountains outside Ruidoso, NM are probably the closest area with an extended downhill.