As Depth of Field is related to the focal length and subject distance; The shorter the focal length the greater the Depth of Field.
Compact cameras have much smaller sensors than full sized DSLRs so shorter focal lengths (wider angle lenses) are needed to get the same framing.
For the same framing and F-stop; a full frame DSLR with a 85mm lens will offer shallower DoF than a crop camera with a 50mm lens. From a quick Google, the LX5 has a crop factor of 4. So, for the same shot you'd have a similar DoF to a 21mm lens on a full frame camera.
Result: Greater depth of field with compact cameras.