What if the card holder is a criminal, too? Would you be happy for the lottery to give £4m to, say, an OAP mugger who hadn't bought a lotto ticket?
Yup. I kind of alluded to this possibility earlier in the thread.
Given that we now live in Broken Britain, you can almost guarantee that the owner of the stolen card will most likely turn out to have a backstory that makes them even more undeserving of the money than the lowlife who stole the card.
Just give the £4m to Great Ormond Street Hospital and move on.