How to manage water pooling at a particular spot in my lawn?
Cut the down spout off about a foot and one half.  Then fix a 45° bend to the bottom of the downspout.  Now install a 3-4' section onto that elbow and extend it out onto the lawn.  The rain water should now dissipate into the lawn before it can find its way back to that low spot. When mowing, set the extension to the side.