Today I made a quick test to see if there is a difference between Jpegs and RAW files and LMO on and LMO off with my Fujifilm X E2 and the 18-55 mm lens.
X E2 Firmware version 1.1, Lens Firmware 3.1 => LMO possible
I tried F-Stops from F2.8 to F22 using an Imatest test chart and a took images of a wooden table from F4 to F22.
I could see a difference between F5.6/F8 with false detail and F11 and F22, getting worse towards F22 - this is expected behavior.
EDIT: Sorry - just realized I messed up something - the difference is also visible in the center of the image - but only for Jpegs.
LMO does effect Jpegs, Raw seems unaffected.