The Home one is a bit tricky, it has this in the parent's style
.front-page .menu .current_page_item a {
background: none;
background-color: transparent;
background-image: none;
filter: none;
}
On a sidenote, the menu doesn't look like it's the one created from WP dashboard under Appearance, it looks like it's the default fallback page menu ( you can see it's sorted alphabetically ), with the Home one being automatically added, this might be the reason there is no class output into the <li>
So as it is now, for the Home one, you could just use :first-child
.menu > li:first-child > a {background:red;}
or with attribute selector like this
.menu li a[href="http://yeahitsfree.com/"] {background:red;}
or this
.menu li a[title="Home"] {background:red;}