LitRpg
I am not familiar with LitRPG except for a webcomic called Artificial Incident. That said, I did some research. Apparently there is no one system of choice for the construction of a LitRPG.
d20 seems to find favor with some, and still other systems find favor with others.
There are resources out there, but I'm unfit to recommend any of them. You might do some research on the subject in your favorite search engine. The search phrase "LitRPG game systems" was especially illuminating.
I suppose the novels of the late Professor M.A.R. Barker could be considered LitRPG of a sort, though he took great pains to conceal the underlying game system from the reader.
Here's wishing your own researches will bear fruit.