Just about anything you want to know about public land hunting in Texas can be found here: https://tpwd.texas.gov/huntwild/hunt/public/
There are region specific maps. The panhandle one is https://tpwd.texas.gov/huntwild/hunt/public/annual_public_hunting/resources/region1.pdf
According to it there is no public land rabbit hunting opportunities in Lubbock county. But if you go north to Hale county there are two locations: Abernathy North and Petersburg. Over in Floyd county there are several: Circle Tree, Bluestem, South Plains, 94 Trust, LSR, and Mesquite Hill.
Unfortunately, while Texas has state-wide regulations rabbits each of the public land units can (and often do) have their own rules for rabbits. The way to find them is to look up each unit on the map ... http://tpwd.maps.arcgis.com/apps/webappviewer/index.html?id=c9788957300943559f7b49206e8ef153
. There will be a download for each unit and that will contain all the rules pertaining to that unit.
For example, the Mesquite Hill unit allows rabbit hunting 1 September through 27 November and then again from 5 December through 29 January (though the entire unit is closed 25 November through 1 December). No mention of means/methods so whatever the state-wide rules are apply here.