What is this black/white pest on my garden lawn?

This is dog lichens,a cross between an algae and a fungus. They develop where turf is sparse or weak so improving/feeding the lawn would probably help.
Otherwise it should be treated as a weed.

My neighbour had a bad bout of this in her lawn a couple of years ago - possibly due to overhanging trees and she treated the area with Armillatox - according to instructions...and aerated the lawn ...and so far - no recurrence. Dog Lichens is unsightly but is curable....there are other proprietary products that deal with it too and if you Google ...you will find them. Good luck.

Treat it as Alzheimer says, but do improve the conditions, and its likely it won't then return. Scarify the lawn now, spike all over by inserting the tines of a garden fork and standing on them, and pulling it straight out again, all over, about a foot or less apart, then, if you want to, (its not essential) apply Lawn Sand from the garden centre.