Thanks for the redesign. Can we have you remove the L and Star and try to keep the pie area contained... something along the lines of #22 (see how the L nearly looks like a pie slice)... I mean make the interior circle look more like a pie chart, with an L as part of the design.
Also, maybe angle the entire logo like #32... Finally, add back the shadow effects you had on #44.
Please capatilize (small caps) the tag line and have it match the width of the company name.
thanks for the effort.