She's not a Sith Lord, but she does know a thing or two about the Sith.
That's my point exactly. Darth Bane was no more a Sith Lord of the Sith Empire or the Brotherhood of the Sith than Nicholas II was a Roman Emperor. From the Imperial Sith or Fraternal Sith perspective, he and his successors were bastards. From the perspective of the Sith Order, they were perfectly legitimate. In the exact same sense, Lumiya is a bastard and illegitimate when viewed from the perspective of the Sith Order; she's perfectly legitimate a Sith Lady as long as you consider her by herself. I don't deny her Sith Lady status. She's simply not a member of the (now extinct) Sith Order. She's no more a Sith Lady of the Sith Order than George III was King of France.
Nope, she doesn't need to keep the rule of two, since that was an edit of Bane's; Palpatine was all but completely flouting it once he was all-powerful anyway. It would probably be a good idea for her to adhere to it though, since the entire point was to keep the Sith under the radar until they were in a position to spring their trap on the Republic again.