Obviously, there is a date/time record of when the ticket was sold. If some other evidence can establish who was at the counter at that time, like store surveillance video, then it is entirely possible to determine the owner.It shocks me to hear the police and lottery officials yapping about "finder's keepers" in this case. It's completely irresponsible.
Treating lottery tickets as anything other than bearer instruments is what is irresponsible. If people have to start proving they bought tickets through other means, the potential for mischief is infinite. Cops can be bribed. Tapes can be faked. The amount of money we are talking about can buy the cooperation of an awful lot of people who will swear up and down that the ticket belong to... whoever...
If you lost your lottery ticket, you lost a buck worth of lottery ticket. Nothing more. 99.9% of lottery tickets are bought, saved, and checked by the person who bought it. Any story that winds up with the ticket in the hand of anybody other than the person who bought it is very unlikely, IMHO.