Your AS miles can be a bit more difficult to use from your area, as AS doesn't serve it.

Yes, AS miles are valid on AA and CO which both serve Lubbock, but AS has a very stingy combinability policy for rewards, as I believe they'll only throw in their metal segments when booking a partner reward.

So, partners such as BA that would require that you get to DFW or IAH would only be bookable out of those cities (you'd be on your own for LBB-DFW/IAH). If you redeem the same award using AA miles, AA will throw in the segment to DFW.