In Pokemon SoulSilver can you breed Lugias?

Answer 1

No. It is a legendary, and legendaries can't breed. No matter what Pokemon you put in the daycare, there will not be a lvl 1 lugia there later on.

Second Answer

But there is an extension that comes with the game, If you get the Nintendo Event Arceus and trade it to Pokemon Soul Silver or Heart Gold, go to the Ruin of Alphs and go inside the house, there will be a man that will take you to the Sinjoh Ruins and you get to pick from Dialga, Palkia, or Giratina and Arceus will make that Pokemon for you to keep and train. You'll see a beautiful short clip then see an egg that hatches into one of three legendary Pokemon you chosen. Becareful and make sure that's the right Pokemon you want. You can go back but you will need an adamant orb, grecieous, or lustrous orb to get the right legendary you want.