Diamond stones work best for me.
DMT Magkit with extra course bought separately.
For the lawn mower, I use the fast metal shaving of a ceramic and tungsten carbide sharpener.
SHARPAL 103N All-in-1 Knife Garden Tool Multi-Sharpener
Just a few minutes with that on a mower blade and your good enough, again.
I have course stones, I never use them since my blades never get that dull