Should we kill the grass before laying fleece?

My father is eldery and has decided to lay stone chips down on the grass to save him having to cut the grass in the future. The level of the grass in terms of the pathway is low enough that we don’t have to take off the top layer of grass. QUE: Should we kill the grass before we lay the horticultural fleece and if so, what should we use? It would be the intention in the Spring to cut holes in the fleece and plant shrubs.