How to Catch Lugia

[Latias1]

I have the Pokemon Crystal Game and I am trying to Capture Lugia he is at level 70 and have been trying the hardest to try and capture him.

[HedgeCat]

I thought Lugia wasn't in Crystal.

[Poryhedron]

No, Lugia's in Crystal. I believe you get the Silver Wing for it in Pewter, while you get the Rainbow Wing for Ho-Oh in the Tin Tower after you catch (not defeat, actually catch) all three Legendary Beasts.
The best way to catch anything (well, okay, the best way to catch anything is the Master Ball, but the second-best way) is to use False Swipe to ensure that it's at one HP, and put it to sleep. Usually, the best way to accomplish this is with a Parasect that had a Scyther for a father and knows both False Swipe and Spore.
Now, Lugia's Flying-type, and in Silver Version, where it's level 40, its Aeroblast can spell doom for a Parasect. But at level 70, Lugia doesn't remember any Flying-type attacks, and Hydro Pump will be ineffective against Parasect, so it might just work. That's my advice, though it'll take quite a while to arrange and you might want to try something else if don't want to take the time to breed and raise a Spore Swiper Parasect to be able to take on a level-70 opponent.

[Strider]

It's a matter of persistence on getting Lugia, really. Do as Poryhedron suggested, and be sure to stock up on as many Ultra Balls as you can afford if you opt not to use, or have already used, the Master Ball.

But if you don't want to go through the trouble of breeding, simply take in a high level Scyther/Scizor with False Swipe. Without paralyzing or putting Lugia to sleep, though, it will take a bit more to capture it, of course.