Joan:Tho it looks like LSU Purple ,inside and out,but more so inside,i,I doubt it is.
Why,Because LSU Purple is very late here and I would think it is later than July 4,for main crop in TExas too.
I could be wrong,but someone from Texas could chime in and tell ,the ripening date for LSU PURPLE in Texas.
If the dates coincide,then it is LSU PURPLE.
Edit note:These are information,from LSU University,about LSU Purple growing in ground in south Louisiana,on university grounds.
It has three crops,(FROM-till)
The first is Breba,between June 30 to 8-18,next is main:Aug 23-Sept 10,third crop after Oct 1st.
Your fig produces fig much earlier.
Unless it produces so early because it is in pot,your fig is not LSU Purple according to LSU.
I have a spare LSU PUrple I would be glad to trade for a layer of your fig,because I need early cultivars here.
LSU Purple 6/308/18; 8/239/10; 10/111/27