I also have a LX2 camera. Except when shooting a macro or a tele
photo, the truth is that it is difficult to judge "bokeh" because
almost everything is in focus.
The LX2 is not going to beat an SLR in this department but; if you do the following:
i) Set macro mode using the switch on the lens.
ii) Use aperture priority mode.
iii) (I think) Zoom in on the subject while moving the lens as close to the subject as you can.
iv) Bottom out the aperture.
Doing this, you should be able to get quite reasonable blurring. I have a couple of examples somewhere - will post them to my Flickr account and do a comparison.
In the meantime, here is one I did with the aperture set to the maximum (as always with me, quite by accident) that nevertheless demonstrates some Bokeh (not sure how that works but I'm sure someone here can explain).
And for an unfair comparison (just not the same conditions), here's one I accidentally got with my D40:
|Hot Air Balloons Over Bagan by User9320321874|
|Yellow Warbler by LeeS|
from A Big Year - birds
|Waiting for the Parade by tcoker1103|
from - La Vida Loca - (Black and White Street Photography+ A Border)