If it is a minor problem, nothing much needs to be done but if a lot of questing woody roots are formed the lawn will eventually suffer dryness and competition for root space. In this case, dig a trench around the lawn, cut all offending roots and place a barrier of heavy polythene to help reduce the roots’ incursions. The back fill the trench.
I have come across a virtual ‘labyrinth’ of roots, just under my back yard lawn (that was rolled lawn laid 2 years ago). The roots are identified by what i had thought were a ‘flowering weed’, however i discovered that they were in fact growths from a series of varying width roots that exist approximately 2 – 6 cms under teh grass surface. I have simply (and quite brutally), used a claw hammer to ‘hook’ the root from the ‘bud’, and then using the hammer, pulled up the root (vary in width from 3mm to 1.5cm and length of 300mm to 1m. The area of lawn is 6m x 7m. There are 2 large trees in the opposite neighbors backyard, but dont seem to be attached to these.
It is quite likely that these roots are from the trees or other trees and shrubs nearby. It is common for tree roots to seek out good soil under a law in the search for nutrients and sometime sthese roots send up shoots as well.