Even Wookiepedia doesn't seem to have this information about the TIE Fighter from Star Wars.
The original TIE Fighter's full model name is TIE/LN.
A friend of mine insists it's "Tie-in". But no. I've always known it to be L not I. Wookiepedia also has it as LN, but no explanation as to what that last part stands for.
The LN model letters you've mentioned were an invention of the Star Wars Essential Guide to Warfare and seem to stands for Tie/Line Fighter; where "Line" indicates that it is the production-line model, one without any substantial modification (e.g. standing apart from the TIE/IN (TIE/Interceptor) and TIE/AD (TIE/Advanced Model), etc.).