In my original LFS folder, both AX_CHALKALPHA and chalkALPHA seem to have the same texture, which contains all the arrows and lines, with an alpha channel. So it is not a blank texture, it only has got transparency.

I'm not sure which texture LFS uses but I'd say AX_CHALKALPHA, because there are 4 relatively new DDS files called AX_something.
Download procces monitor and make a filter path to your dds folder , turn on your game and while editing in shift +u mode it will hopefully give you the list of files you need . I use this when ever i make textures for tracks and i need to know the complete list of files to that track .
it's not like demo users can see the autocross chalk texture anyways.

FGED GREDG RDFGDR GSFDG