Assigning a class to children

I’m hoping someone can help me with this. I’ve spent a few hours on google and am still coming up blank.

I am creating a custom for our school’s web page where each menu button and the drop down associated with it are unique colors. I have a html prototype here.

I am trying assign each of the parent <li> and the entire child

to a css class (the only css code for menu1, menu2, etc. is only color).

<ul id="menu">
        <li class="menu1"><a href="#">Administration</a>
            	<ul class="children menu1">
                  <li><a href="#">Subitem 1</a></li>
                  <li><a href="#">Subitem 2</a></li>
                  <li><a href="#">Subitem 3</a></li>
                </ul>
        </li>
        <li class="menu2"><a href="#">Schools</a>
            	<ul class="menu2 children">
                  <li><a href="#">Subitem 1</a></li>
                  <li><a href="#">Subitem 2</a></li>
                  <li><a href="#">Subitem 3</a></li>
                </ul>
        </li>

I know how to control the li classes through a custom walker class but am completely stuck on adding the <ul class="menu1">.

Thanks in advance for any help!