The oil isn't necessary, but it is desirable. To say it will be too tough without oil is rather subjective. The first rule to following a recipe is to follow the recipe. If you don't like the results, go back and modify it.
Also, assuming that you are using Caputo 00 Extra Blu flour with 9.5% protein, and King Arthur Sir Lancelot flour with 14.2% protein, you may find a mix of 68% KASL and 32% 00 to be more like bread flour (12.7% protein), but like I said, follow the recipe first.