Is there anything I can do to get money from overlooked winning lottery ticket that a coworker cashed in for $440,000?

Do you have the purchase receipts for the tickets? Does your receipt match the place and time of purchase on the winning tickets? Also, look through your other tickets to see if you still have yours. If you do find receipts that match up with the winning ticket, speak with a lawyer in the State that runs the lottery. Other factors that might be evidence that the winning ticket was yours is if it was purchased where and when you always buy your tickets and if it used the numbers you usually picked. Also, most stores have surveillance cameras. Lotteries are so precise now that they can pinpoint the date and time the tickets were purchased. Surveillance video may show who bought the ticket. If all these things show that you bought the ticket, there will still be the question of whether you were purchasing it for your business partner, or if you knowingly transferred the ticket to him as a gift or payment.

If you threw the ticket away and intended to do so, you probably don't have any claim to the payout. You would need to prove that you bought that particular ticket and did not intend to lose it or misplace it and that your co-worker took it while knowing it was a winning ticket.