Right on about placing tickets in a "safe place" or somewhere else that is specially dedicated for lottery tickets, so they can be found without a problem.
My only reservation about keeping them in a vehicle, is that if there is a fire they could be destroyed, or if the vehicle breaks down and needs a tow, they could be picked up bysomeone other than the owner of the car or truck.
Yours Truly, removes them from the bill fold after getting home and places them in one spot on the dresser.If the tickets have any prize money, they go back to the bill fold to be redeemed next time at the lottery vendor.
After they are checked then they can be moved somewhere else, if you keep them, for a tax write off, in the event you hit a big jackpot. Know most folks just throw them away after checking them.
Every one has their own way of keeping track of their tickets, no doubt. You just want to make sure the kids or pets can't get access to them. Used to have a dog that loved to eat paper.