I wondered if the tags Lucas Sequences and Basis might be of use? I imagine these would be sub-tags of sequences-and-series and linear-algebra.
There are a total of 25 questions containing the words "Lucas sequence", and more than half of them are actually talking about the Lucas numbers, which there's already a tag for.
Granted, many people don't know what a Lucas sequence is or even how to pronounce "Lucas", so they might be talking about Lucas sequences without calling them out by name. But if that's the case, then they're not going to be using the proposed tag, either.
And if both the lucas-sequences and lucas-numbers tags existed, then we'd have to sort out the extra confusion caused by people using one when referring to the other, too.