i think you are misunderstanding 2 tasks in grunt,
the connect task is used to create a http server spawned by node js, so no php nor mysql support, you DON'T want to run you WP site thru that.
the watch task is looking for changes in files on YOUR computer, launching the according task after a file change, then trigger the live reload.
you should remove connect completely after you copied the live reload object in your watch task.
the you should run your local lamp stack for running wp then start the watch task for file changes.
on the wp side you should enqueue the live reload script, or use a browser extension that will inject it for you.