First off, checking whether 'I Am the Luna' is finished is always going to lead you into the wilds of Wattpad serialization. The story's status isn't always clear-cut on the platform itself. Last I looked, the author had marked the main story as complete, but then there was a sequel or an extended epilogue floating around that seemed to get sporadic updates. It's one of those series where the core conflict wraps up, so you get a complete narrative arc, but the author sometimes pops back in with bonus chapters focusing on side characters or future glimpses.
Honestly, if you're waiting for all possible content to be absolutely, finally done, you might be waiting a while. The nature of web novels means authors can revisit. For a full and satisfying read, though, the marked 'Complete' version gives you the whole Luna journey from start to finish. Just be prepared that the 'On Going' tag might reappear if the muse strikes the writer.