Fairy Tale is a long-running manga series. I haven't been following (I dropped the anime after 100 episodes or so) but generally for this kind of series, if a character is declared to be 17 at the start of the series, they are just going to be 17-ish more or less forever. Regardless of the fact that you can count New Year or birthday episodes to find a higher number, they're still going to act like and be treated like a teenager until and unless the plot calls for them to grow up, e.g. to introduce a new generation of characters. Or because the series is ending and they finally want to complete the character development they've been hinting at.
You are not going to be able to "prove" Lucy's age (or any character's age) with these kinds of language details because manga usage isn't real life usage.