The problem is the complicated pivot design of the LCC. Mine had quite some blade play as well, and fastening the pivot screw didn't help at all (is is secured with loctite, by the way).
Set into the blade is a bushing of hardened steel that is just a tad wider than the blade, so you cannot tighten the pivot too much (or enough, in some cases).
The bushing of my LCC was clearly too wide, the washers didn't fully touch the blade, and the bushing stopped me from tightening the pivot. So i diassembled the knife, took the bushing out and gave it a few strokes on my sharpening stone. This is a somewhat delicate operation, you have to remove VERY FEW metal only.
After that i reassembled the LCC, and lo and behold: The blade play had disappeared. The action was a bit stiff at first, but after some time it became perfectly smooth again, still with no blade play.
It's not something for the faint of heart, and you may want to check other options first (i heard sometimes shortening the pivot screw with a few file strokes does the trick), but the only other option is sending it back to microtech.