Hi CeeKay and welcome to the forums.
The term you're describing is known as depth of field, which is controlled in the main by two variables. Firstly the size of the aperture you're using and secondly the focal length of the lens. You would use a small aperture (larger f/number) and a focal length of 14mm - 25mm for a shot of a sweeping landscape to keep both the foreground and background in sharp focus. If you're taking someone's portrait you would use a wide aperture (small f/number) and a focal length of around 80mm - 120mm, to blur the background but keep your subject in focus.
What you are looking for is a camera that is capable of giving you a shallow depth of field. The question is can the LX5 deliver a depth of field that is shallow enough for your purposes? The only way to answer that is to physically try it for yourself in a shop. Set up a test shot in the camera shop where you take a close up (macro) shot of another camera they have on display. Set the LX5 to A (Aperture Priority) and zoom the lens in to it's maximum 90mm focal length, get in close to the subject and take some test shots. Examine the shots it produces and make a judgement call. If it doesn't blur the background enough for you then you either don't buy it or you'll have to blur the backgorund using a post processing photo editing software package.
You may find that because this camera is a compact that the sensor is too small to give you a really shallow depth of field, whereas something like the Sony NEX5 with an APS-C sized sensor ( approx 18x larger sensor than a compact) or a Panasonic G2 or Olympus EPL1 with a Micro 4/3rds sensor (approx. 12x larger sensor) will do this more easily for you.
Hope this helps.