Ok, so I just recently finished Happy Strike and decided to add it to the site since there wasn't a series page to it nor any mention of it here. As it turns out there's 4 of them in total in Comptiq version(?)
I think the associated names section's going to be messed up but I'll keep it like the Full metal panic novel page for now.
The first of this series was published in 2007 as stated above, so Happy Strike was the first, not Lucky Turn.
As for how this set relates to the main Lucky Star, I'm at a loss since this goes on its own slice of life pace that lucky star has and they're still in the school and cast. The only difference is that it's not in the 4 panel form but regular manga panels.