Your problem is that a div has no src attribute, as in your example you have <div id=loadImage></div>

Your defaultImageurl is also empty.

The solution is to use an <img/> element:

var customImageurl = custom_Image/web.png;

var defaultImageurl = ;

function loadGraphics(){

    //v-- will not work! 

    document.getElementById(loadImage).src = defaultImageurl;

    //v-- will work given your example conditions

    document.getElementById(loadImage).src = customImageurl;

}

window.onload = function(){

    loadGraphics();

};

<div id=loadImage-wrap>

    <img id=loadImage />

</div>