Hello David, have you tried some lawn weed and feed? You water it in, I think, and it does the job for you. If there's a lot this weed you may need to seed the bare patches afterwards, but you'd have to leave it for a while to let the weed killer die down. There should be instructions on the packet, anyway. A picture of the weed would be helpful, so that we could identify it and then be more helpful. With some weeds you can just dig them out with a narrow trowel, but others have long tap roots. Hope this is helpful. You'll get the lawn weed killer from any garden suppliers. Good luck with it, Annie (Cumbria)

Thorny? could this be thistles? or you may have suckers coming from a tree or shrub nearby? A photo would help?

Perhaps you mean brambles ?
These thorny, spiney runners will invade a lawn (or border).
They could well be coming through from the neighbours garden - i'd be inclined to apply a spot application of weedkiller onto the foliage (use newspaper to protect the other area).

If you have a pyracantha nearby, particularly if used as hedging, the thorny shoots maybe coming off the roots if they've extended into the lawn.