Limes and lemons are typically flavors found in carton drinks; for whatever reason, they're not popular fruits for solitary consumption (though I happen to like both limes and lemons). I was speaking the other day with someone who uses lemons, and only lemons, frequently as a cooking ingredient. I was surprised when she asserted that limes and lemons are the same fruit. Obviously, this is not true; she backtracked and asserted instead that limes are just "unripe lemons".
While there are nutritional differences between limes and lemons I won't disclose here, the fact remains that saying limes turn into lemons is like saying windows turn into doors. Limes and lemons are completely separate fruits. A bit of research will turn that up. This cooking site, for example, briefs the reader about common misconceptions. The reader will learn that limes are not unripe siblings of the lemon. In fact, the lemons we buy at the store are also unripe. Both limes and lemons are unripe fruits. If you wish to know more about these beloved sour fruits, I advise you to do some more of your own research. Hopefully, you'll be spared the embarrassment of ever saying limes and lemons are the same fruit in public.
As for me, I favor the lime a bit more than its yellower cousin. Limes don't have seeds and are a tad bit sweeter than lemons, making them the more delicious of the two to my taste buds!