Lugia can be caught at Nickledark Island. He comes out at level 50 after you defeat Cipher Boss Deathgold. To purify Lugia, get full tempo in all nine chambers. Then, place Lugia in one of the sets and it will be purified.

To get an opportunity at snagging Lugia in the demo version, you must first snag the first 60. Then, go to the mountain with a Groundon statue and Lugia will fly there. You will them battle him; he is at level 50.