I have worked in many Mexican restaurants with Spanish native speakers from Mexico to South America, and I have worked in upscale restaurants where the majority of the kitchen was of the same makeup, like Country Clubs, etc ... Chefs, trained chefs, (one in particular a Gold medal winning native Spanish speaker), will sometimes make a distinction between a "Yellow lemon", (inedible when unripe or green), that never changes to green, (what we see in the grocery store here in the States), and a "Green lime" that will eventually ripen to a dusky yellow but is totally edible, and sometimes preferred in its mature, yet still green condition. Limes are small, lemons are mostly larger. But even trained native Spanish speaking chefs don't particulary take pains to distinguish between them verbally. They are all "limón" but sometimes are qualified with size and color words. In rare cases, I have heard chefs and their cooks and staff get a bit frusterated with one another when there are both "American lemons" and "small green limes" in the same kitchen and there is a person asking for "limes". But usually, whatever is requested, a lime, or a lemon, invariably one or the other will be hurled at you, especially if you are a waiter or working on the front end.
That's exactly (minus the specifics) where I got my information, too. During college I waited tables and would often practice Spanish with the guys cooking in the back- and it was great for comprehending the vast differences between Latin American dialects and accents when they would argue about what vocabulary I should be learning. But they all pretty much called limes and lemons "limón", so I'd need to ask specifically for a green one or a yellow one. It was a nice restaurant, but we didn't have any medal winners, which is possibly why I didn't get the level of distinction in conversation about it like you did.