Now that you have this, and the Rainbow Wing (Gold) or Silver Wing (Silver) from the Radio Tower Director, you can go catch Ho-oh (Gold) or Lugia (Silver).

You better save your game before fighting Ho-oh, because like Mewtwo, there is only one. Try getting Ho-oh down to as little HP as possible, and put it to sleep. Ultra Balls should do the trick.

Go to Olivine (Asagi) City and surf south trying to stay as far to the right as you can. There is 4 entrances to the cave where Lugia is so if you follow the wall the first one you come to is the one you need to enter.

Once inside go to the right and choose the top path when it comes to a fork. Now you'll make your way to a waterfall, go down it, then surf up and you should find Lugia swimming in the water.

Lugia is also level 40 and will give you 1257 experience points if you beat him. But DON'T, what are you crazy or something!? Again, low HP, asleep, and ultra balls should do the trick.

But first make sure you have a Pokemon with Surf and Waterfall. And heal all your Pokemon in Elm's Lab.

Next it's time to surf east from New Bark (Wakaba) Town.