What links "Luluco Space Patrol" and "Kill La Kill"?
My question is: what links those two shows? Same editor/writer?


Same everything, pretty much. Both shows are original IPs by Trigger (the animation studio), directed by studio founder Imaishi Hiroyuki, and I assume that many other staff members worked on both shows.

Trigger (or maybe it's just Imaishi) is known to be fond of reference humor - there were, for example, oblique references to Kill la Kill even in Inou Battle wa Nichijou-kei no Naka de, the latter of which was an adaptation of a non-Trigger IP. Given the opportunity to reference one of their own IPs from another of their own IPs - which means they don't have to tiptoe around copyright issues - the results are what you see in episode 7 of Space Patrol Luluco.

In addition to the Kill la Kill thing in episode 7, there's also Little Witch Academia in episode 8; Sex &amp; Violence with Machspeed in episode 9; and Inferno Cop in episode 11. These three things are also original Trigger IPs.