No. International baggage is never checked through to its final destination when transiting in the USA*, and it must be collected at your port of entry so that you can proceed through customs with it.
When you arrive at DFW, you will clear immigration, collect your hold luggage, and then pass through customs. After customs, but before entering the public area of the airport, you will find the AA baggage re-check desk. You will give them your hold luggage, and then enter the public area of the terminal. You can then walk or take a bus to the terminal your connecting flight leaves from, and pass through security. If you somehow miss the baggage re-check desk, you can leave your hold luggage at the appropriate check-in desk.
When you make the return journey, assuming the booking is a single ticket, your baggage will be checked through, and you will only have to clear security once, in Lubbock.
*Unless the airport you're departing from has pre-clearence, which it doesn't in this case.