Is The Melancholy of Haruhi Suzumiya anime related to Lucky Star?

yes, both of them are made by 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 Youtube & Nico Nico Douga years ago, it wasn't hard to find out that the series were connected.

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

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