well first you get to the Kanto region by beating the guy on mt. silver then there is a town called pewter city. In pewter city you will get the feather from the old person right next to the poke mart.
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In heartgold, Lugia is obtainable at the Whirl Islands but u need to obtain the silver feather from a guy in Pewter City. Once u have that silver feather, u can go deep into the Whirl Islands and find Lugia.
You get the silver feather from someone in Pewter city. From there, you can catch Lugia at Whirl Islands. He'll be level 70.
A person in Pewter City will give you the Silver Feather, then go to Whirl Islands. When you get to the end of the cave you will see Lugia.
that Pokemon is located in mt. Silver
you cant but you can trade it from Pokemon soul silver