There is lots of mineral in the soil but most is unavailable and does not show up in a standard chemistry test. Biology slowly breaks soil mineral and residue down, and makes it available in what is called "mineralization cycles". Grazing accelerates this soil biology as a function of stocking density, temp, moisture, type of plants growing... This is one of the reasons grazing gurus are so hot for mobs grazing cover crops. It improves several factors at the same time.
Biology is NOT linear and you need to make this work for you. Some ways to increase soil fertility quickly when you have very run down ground with limitations is to kick start the sod biology:
1) spread manure, and then pound it with cattle
2) bale graze, and then pound it with cattle
3) lime, and chemically fertilize the limiting factor to a moderate level, and then pound it with cattle
Lime clumps are not helping you. Tillage is usually used to work lime in one or two years before reseeding. I have run a drag after nasty bi product lime was spread on sod and it had dried, but cows would be happy to pound and piss on lime clumps for free...