I had one lost OWE ticket which was issued by AA so I had to deal with AA for the replacement. This takes 90 days -- to the day -- and in the interim you pay for a new ticket. So you are out the dollar cost of the tickets for 90 days (pretty hefty float). I was told this 90 days is how long it takes to ensure that the lost ticket has not been used elsewhere in the world. In the days before security it was quite easy and common for the pax flying to not match the name on the ticket, I suppose. In any case that was my experience with a lost ticket. Treat it like cash; losing it is more than just an inconvenience.