The writers haven't addressed this in the story or in any footage (that I can find on the web). I will make a correction in my thinking, though. I deduct that Lin is what you might call a "half-sibling" to Suyin, who is possibly and very likely the daughter of Satoru. The two latters are overwhelmingly similar. Their very dark or tan complexions; their interests are similar; the very coarse and textured/curly hair; amongst the fact that Toph and Satoru appear to remain very close in the continuation of the Avatar: TLA series. As I explained my thinking earlier, Satoru really helps Toph out by financing her BMA, and even prior to this, Toph shows strong interest in many of the processes happening at his [uncle's] refinery as well as his technological prowess and accomplishments, thanks to Aang. I advise you to go back and read the since comments and let me know what you think. I feel that Lin, due to her lighter complexion and the fact that she is nothing like Satoru in any way, may very likely have a different father, possibly from the Earth Empire. Of course, this is fiction and therefore "real" genetics can't truly be involved, but I look at the way each nation looks. Airbenders and Air Nomads are the fairest of the four nations. Following them are Fire Nation, and following them, as I'm sure you know, are Earth Empire Citizens. The darkest of all by far are Water Tribe. Therefore, we can base our judgments by how the daughters look, and I strongly *think*, and deduct, that Toph may have had multiple sexual relations. :)
Regarding Lin appearing to be nothing like Satoru, could it simply be that they each took after a different parent? Toph claims Lin's father was named Kanto, but that seems more of a fire nation name than an Earth Kingdom one. I say this because Kanto is a Japanese name, and those are associated with the Fire Nation more than the Earth Kingdom. While a few more recent EK characters have Japanese names (Kai, Ryu, etc), Kanto is the name of a region of Japan as well as a name the Japanese Imperial Army gave to an area of Northern China. Also, in the Avatar world the children of interracial couples have sometime been shown to take completely after one parent. In the case of Katara and Aang, Tenzin looks almost completely like the Air Nomads of old (except his eyes) while Kya looks completely Water Tribe. So, maybe Lin just took more after Toph with her appearance and tough persona while becoming cynical and bitter due to her various heartbreaks. Also, Toph's strong relationship with Satoru has made me wonder why she would have a child with someone we'd never heard of before and then have a child with him (who she knew first).
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