Either the GX1 or G3 will be much better than the LX5 or other compacts, equivalent to a Canon 600D or Nikon D5100.
The GX1 does not have a built-in viewfinder, like the LX5, so can be difficult to see the LCD in bright sunlight, and not much larger than a LX5. There's an optional viewfinder for abt $350. The G3 has a built in finder but less compact than the GX1. The G3 is about $800 while the GX1 is a bit more, but without the viewfinder. IQ about the same.
Which one is suitable for you very much depends what your expectations of a camera are. I have the GX1 because I prefer the small size but I also have a GH1 when I want to shoot with long lenses and need the VF.