There are others who are perhaps better qualified than I to address your question, but at high oil levels the flour in the dough is prevented from being fully hydrated (reduced cohesion between wheat gluten strands), leading to reduced gluten development (the gluten needs good hydration for development). So, the gluten strands will become less elastic and the finished crust will be tender. To the extent that solid fats are used, like butter or margarine or shortening, their use will shorten the length of the gluten strands (hence, the term "shortening") and contribute to flakiness in the finished crust. As you reduce the amount of oil and/or the solid fats in a dough formulation, you should expect to experience more gluten development, because of more complete hydration, and less flakiness or biscuit-like effect. So, the crust will start to approach that of a crust made from a more standard dough. An additional effect of reducing the amounts of oils and fats in a dough is that there will be some loss of flavor, since one of the purposes of using oil or fat in a dough is to get the flavor profile and richness that they contribute. There will also be a reduced fat "mouthfeel", which some people find very desirable. Of course, the caloric count will be down also.
The amount of oils and fats to use is, to a great extent, a matter of personal taste preference and also what kind of texture in the finished crust you would like to have. Hence, I can't tell you where you should draw the line in your case. If I were trying to draw that line for myself, I would perhaps start at the low end of the range and compare the results with higher oil and fat values. Remember, too, that reducing the oil in a given dough formulation will also require adjustment of the hydration of the dough, with effects that may not be known, or even liked, until you try out the final formulation. That is why I personally would look for an existing deep-dish dough formulation that uses low levels of oils and fats. Even then, you should be able to use some semolina flour as part of the overall flour blend. I did a quick search and found a Tom Lehmann deep-dish dough recipe at http://www.pmq.com/recipe/view_recipe.php?id=54
that uses low oil levels. Surprisingly, the amount of oil is even lower than the lower limit I mentioned in my last post. Another fairly low-oil deep-dish dough formulation is the one that appears at pages 130-131 of Peter Reinhart's pizza cookbook American Pie
. That recipe calls for 5 tablespoons of corn oil, with an estimated baker's percent of around 11%. However, I should caution you that my recollection is that some of the members did not care for the Reinhart recipe. Of course, that doesn't mean that you will react the same way to the Reinhart recipe.
Edit (2/15/14): For a replacement for the above inoperative link, see http://www.pmq.com/Recipe-Bank/index.php/name/Deep-Dish-Pizza/record/57725/