I'm reviving the ancient game of Pokemon XD: Gale of Darkness. And I am wondering how to purify Lugia, if possible, so I transfer and such.
You can only purify Shadow Lugia by putting it in the Purify Chamber. The purification will be instant. However, all 9 Sets of the machine must be running on max efficiency.
Source: http://bulbapedia.bulbagarden.net/wiki/Shadow_Lugia#History and experience.
You purify Lugia the same way you purify any other shadow Pokemon.
Source: the bulbapedia article about shadow Pokemon (it had stuff about lugia but didn't say anything special had to be done to purify it)