Is The Melancholy of Haruhi Suzumiya 日本动漫 related to Lucky Star?

yes, both of them are made 由 Kyoto Animation

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 youtobe & Nico Nico Douga years ago, it wasn't hard to find out that the series were connected.

Yeah they are. Both were made 由 Kyoto Animation, and Lucky 星, 星级 had a ton of references from The Melancholy of Haruhi Suzumiya. People were saying that Lucky 星, 星级 was an advertisement for it, but personally I loved Lucky Star.

Both are made 由 the same company and Haruhi and Konata have the same voice actress hence Konata cosplaying Haruhi.