For many, many years I've not fed my lawn with stuff from a bag, and my grass is doing quite well. I'm no chemist or botanist, but the results speak well for feeding your lawn naturally in the fall. The health of my lawn, and of my clients' lawns, attest to it.
For years I've mowed my lawn, leaves and all, a couple of times each winter. Basically, this shreds the dead, fallen leaves into tiny pieces (about the size of a dime), which decompose more rapidly into organic matter and add a lot a carbon and other nutrients back into your soil. An added advantage is that the decomposing matter will attract birds like crazy; to pick through the leaf-bits in search of food.
In a very short time the tiny pieces of decomposing leaves will disappear from view, as they filter down between the blades of grass and become part of the soil. This replicates the process that happens naturally in a forest; but does it in a lot less time. This eliminates a lot of leaf-raking too.
(if you're worried about "thatch" - don't be. Thatch, a very rare occurrence, is almost always a fable told by people who want to sell you something)