Also how do you get a Mystic Ticket?
The event has passed, so you cannot receive the ticket anymore. Sorry.
As for Red and Green, you can't even catch Ho-Oh and Lugia in those games.
You may not be able to catch Lugia and Ho-oh in those games, but if you have Pokemon coloseum you can get Ho-oh and the 3 beasts and in Pokemon xd you can get Lugia and the 3 birds. That's how my brother managed to steal my Lugia(xd) for his Emerald when I wanted it for my Sapphire. I stole it back by transferring it into my Diamond's Pal Park.