School comedies aren't really my thing. (Says the woman with using a school comedy for an avatar).
However, I really liked their OPs & when those went mega viral on यूट्यूब & Nico Nico Douga years ago, it wasn't hard to find out that the series were connected.
Yeah they are. Both were made द्वारा Kyoto Animation, and Lucky तारा, स्टार had a ton of references from The Melancholy of Haruhi Suzumiya. People were saying that Lucky तारा, स्टार was an advertisement for it, but personally I loved Lucky Star.