A couple months back I bought a Quiltsmart Lone Star kit. I thought I was buying a 6 x6, turns out it was a 4x4 with instructions for the 6x6. So my question is .... Has anyone purchaced the 4x4 and if so could you please tell me how big to cut the background squares. Thank you!

the kits usually tell you exactly what size to cut everything- i just finished one (but i'm at work- the pattern's at home)
it said precision is needed when cutting and told me the exact size to cut each piece i needed to complete it- and i am so happy with it---every point matched up beautifully and it is one of the best blocks i've ever constructed!
just follow the instructions in the booklet that came with the kit

You should be able to tell from looking at the interfacing - you can see the placement lines.

I vaguely remember 2.5"x 5.5"

Call Quiltsmart - they're lovely to deal with.
Phone: 952.368.3000 (Minnesota)

Those measurements kind of make sense - the 6x6 is 20" larger than the 4x4 LS.

I made four Lone Stars using this method.
It take all the hassle out of making the sections.
I did NOT put it together the way the instructions said though, as I wanted a much more interesting look.
So I put them together like a traditional LS, y-seams and all.
Here's one:
http://www.quiltingboard.com/t-127778-1.htm#3397137