The mistery is his backstory. He's using a mask because he's wanted to be an unknown person doing his job as a killer. It's just that Pai somehow could knock out his mask.
Well, there is other theory that it could be Lei Fei. Historically, Lei-Fei is an assassin from a Shaolin sect who sought to steal Lau Chan's forbidden technique. But that theory is failed to explain why Pai Chan is surprised to see him.
I was going to include him on my list, given Pai Chan and Lei-Fei may have crossed fists during the previous tournament. But given Lei-Fei's Shaolin sect was to be rid of all those who mastered Tiger Swallow Fist, it seems strange for him to give up his Shaolin ways and take up impersonating Lau Pei. Also, Lei-Fei was impatient! With Lau Pai's slow methods and his ailing health, Lei-Fei strikes at his master, thus its one thing to learn a style of martial arts like Tiger Swallow Fist, but he did not learn to master it like Lau Pai.
Two people can make the same chocolate cake, but there may still be variation of taste and texture between cakes depending on baking methods even if the ingredients and instructions were same.
I can accept if Lei-Fei was never right in the head to begin with. He seemed rather aggressive for a Shaolin monk, and taking Lau Pai as a master to learn Tiger Swallow Fist when he was trained to execute Lau Pai and rid of Tiger Swallow Fist from the world instead.
And maybe, he would go as far as let his hair grow long, style himself after Lau Pai and be a murderer which completely goes against Shaolin teachings. But Lei-Fei would only have so much genuine Tiger Swallow Fist skills to go on that it would be impossible for him to recreate Lau Pai's fighting style given how impatient he was to learn it.
