This is indeed a licensed game based on Lucky Star.

I've actually beat this six times before logging it, but I wanted to say that I've truly completed it once I got the Net Idol Meister ending with at least one character. I don't recommend this to anyone that isn't desperate for more Lucky Star content. This game is repetitive and stupidly luck (lol) based, and you have to choose between playing the same three minigames or dumb quizes that I can't understand because I don't know Japanese.
I still like this game, though. It's filled with a ton of fanservice for fans of the series, nearly every bit of dialogue is voiced by the same actresses from the anime, and there's funny costumes and references. There's also a ton of characters, so you'll be playing this for a while if you want to see everything it has to offer.

Highly recommend playing this on emulator if you want to finish one playthrough in a reasonable amount of time. I'm going to keep playing this game and will write another review once I have just about everything.