http://www.ourmanga.com/Naruto/500/04
Mito was able to seal the Fox within herself because she had the Uzumaki clan's revered Sealing techniques, and also the formidable chakra/life force of the Uzumaki. So yes, her lineage was critical.
It's likely that someone with Uzumaki-level chakra would be needed to house the Kyuubi, and the highest level of sealing jutsu would also be necessary. That's why Konoha needed Kushina, even though Konoha's residents are the descendants of Senju (and thus the Sage). However, the Raikage also stated that the Kin Gin brothers were (possibly) distantly related to the Sage, and that's why they could withstand the Kyuubi's chakra. If that were true, it would mean their lineage was less watered-down than the majority of Konoha.
Also, in response to your earlier post, the Rikudou was the first Jinchuuriki, technically. Mito might have been the first in more modern times (Hashirama himself distributed the remaining Bijuu to other villages).
However, it seems that other villages had different methods of sealing / wielding the Bijuu, so the Uzumaki/Rikudou seals are not the only ones that work.
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