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.

Bayonetta: Oomfie Edition is so good. At first I was hesitant due to the control scheme being much different from the mainline games, but it's quick to get the hang of. It doesn't go "guys remember the other Bayonetta games?" at all until maybe the end, but it's more of a reward for being able to make it so far than pandering. My only complaint would be the map. I'm not sure what direction it's trying to point me towards half of the time to be honest, but I'm also stupid so who knows. There's also not too many voice clips so bosses will repeat themselves often.
Art direction is solid, gameplay is too. Cereza's voice actress is really good. I like when she says "Cheshire, over here!"