The "secret project" that Ragecry is mentioning is one that was tweeted by Shoji Gatoh in January 2012. I broke down the 5 tweets he mentioned in
this post. As of right now we do not know if KyoAni will be involved in this project or not.
Secondly, there is a very very very very very very very slim chance (less than 0.001% IMO) that KyoAni will be working on the Lucky Star spinoff anime. You are correct that Yutaka Yamamoto (who was the original Supervisor on
Lucky Star before he was removed from the position after 4 episodes and was a co-supervisor with Tatsuya Ishihara on the 2006 version of
The Melancholy of Haruhi Suzumiya) was on the ema at the shrine, but he is now in charge of the animation studio Ordet (who has also re-tweeted news about the series). Yamamoto left Kyoto Animation in 2007, so why would he re-contract with the studio instead of using his own studio to animate the show? That is why I feel it's such a slim chance that's their next project.
As of today, February 19, we do not know what is the next project coming from Kyoto Animation. There's many rumors going around about anything from new
Full Metal Panic!, new
Haruhi, new
Lucky Star, new Kadokawa properties, new original content (
Beyond the Boundary), etc. Any one of those could be right or all could be wrong. We don't know anything for certain at this moment.