She calls him her Dad, they have a great relationship and he's very supportive. Who needs anything else? Lisa doesn't use his last name, the one both her parents have, which suggests there was another parent at some point.
But if she turns out to be half white, it wouldn't be the gotcha some of you think. Most of her abuse in Korea is racial because she's SEA. Finding out she's whasian would instantly raise her status there. And the "pure Thai" cult is her western fanbase who would just course correct in the way KPop fans are expert at, to celebrate her Swiss heritage. So just mind your business!