Unless you actually find some insects, I think it is a waste of money spraying.

The wood has that sort of look of something in the advanced stages of death - when there isn't much sap transport the wood has a pinched, dried up look to it, and yours has that sort of look to it. (Though I could be quite wrong, maybe it's just the photo.) Things dying of fungal disease look like that. When they get to that stage, they are generally unsaveable, unless you can cut back to healthy wood, and you say the whole plant is affected.

The "frilly" bits of white do look very like lichen, but we'd need a close up to be sure. But there are other bits of more general white on the thing, on the small branches, that look more like some kind of fungus.

Sometimes individual plants do randomly succumb to disease and once it is advanced there isn't much you can do about it. In general, cotoneasters are exceedingly robust plants that are very unfussy about conditions (well maybe they don't like it waterlogged, I've never seem them tested by that) and need a lot of hacking back to keep them under control. So, one has (maybe) got fungus and died. I'm forever pulling volunteer cotoneaster seedlings up, maybe you'll find one that can replace it. Or maybe the adjacent ones will grow out to fill the gap.