(posting as a second answer as it's unrelated to the original)
Based on the last line and the most recent hint, it seems like the answer should be:
14. Or possibly, "What is six times nine?" from the Hitchhiker's Guide to the Galaxy.
but I'm struggling to fit that into most of the puzzle
Google cannot find me
If you google the Ultimate Question of "What is six times nine?" you won't get the answer of 42. Or if you google 14, you won't get just 14 answers. Both of those seem a stretch though
reflected I'm lemon and lime,
Presumably a reference to a well known lemon and lime drink, either 7up or Sprite.
From the Line 2 hint
a fairy's competitor would seem to indicate sprite. Not sure how you reflect that vertically though.
googling 'me' is when you fall,
me and meme will answer all.
14 and 14 doubled gives 42, the answer to life, the universe, and everything
Line 4 last 2 words is pretty much spelling out 42, while also pointing out that it's the answer to all.