How to save Omelette from breaking while keeping the oil quantity low?
You don't necessarily have to increase oil quantity, you have to reduce friction. There are a few variables to consider:


Tools - What type of spatula are you using? If it is a thin spatula, I have found that this increases the likelihood of breakage. I prefer one of two methods; 


use a wide rubber spatula or 
Use a fish spatula

Method - There are numerous methods of omelet making out there. Some chefs, myself not included, add the egg mixture to the heated, oiled pan and then whisk the product to speed cooking time. While I understand the allure of this method, I don't prefer it. Personally, I use what I call the "lift and drip" method whereby I use the spatula to slide the omelet away from the side of the pan, lift the pan toward that side, and allow the egg mix to drip into the void created. It makes a slightly thicker omelet, which reduces the likelihood of tearing.


There are other variables that may come into play, as well, but I don't want to divert too far from your question. So, that being said, my personal method is:


Heat pan to just over medium heat, approximately 105 C (220 F)
Add lubricant (Personally, I use vegetable oil because it's cheap, but I keep it in a spray bottle for better coverage and less pooling)
Allow the egg mix to sit unfettered for forty seconds, or so
I use the lift and drip method mentioned above until the omelet is about 70% cooked
I add any other ingredients (chilies and onions since the salt should be mixed into the egg already)
Then I finish the omelet under the broiler/salamander until 95% done
Remove from heat, plate by sliding one side out and using the pan + gravity to fold, and serve


Be advised that this is indeed for an American bi-fold omelet, not a French tri-fold.