Hello Georgia. Achieving a clean, tender fried egg on low heat with minimal fat comes down to gentle temperature control and utilizing steam.
First, your choice of pan is essential when trying to keep added oil to an absolute minimum. A quality nonstick skillet or a well-seasoned carbon steel pan works best. Preheat your pan gently over medium-low heat for about two minutes before adding any fat so the heat distributes evenly.
Next, measure out just a small amount of oil, butter, or cooking spray (around half a teaspoon is usually plenty). Use a silicone brush or a paper towel to spread the fat evenly over the surface so there are no dry spots where the egg can catch.
I recommend cracking your egg into a small ramekin first rather than directly into the pan. This lets you inspect the egg and allows you to slide it smoothly into the pan without breaking the yolk or disturbing the thin layer of oil.
Once the egg is in, turn the heat down to low. The whites should sit quietly without rapid sizzling or popping. To finish cooking the top of the whites without needing to flip the egg or baste it in excess oil, add about one teaspoon of water around the perimeter of the pan and immediately cover it with a tight-fitting lid. The steam will cook the top of the egg white in about two to three minutes while keeping the yolk perfectly runny.
Once the whites are opaque and set, remove the lid and use a thin, flexible spatula to gently guide the egg onto your plate.