Add the runat=server tag
<ul>
<li class="current" id="myLI" runat="server">
<asp:Button ID="ButtonSubmit" runat="server" OnClick="ButtonSubmit_Click" Text="Submit" />
</li>
</ul>
code behind
protected void ButtonSubmit_Click(object sender, EventArgs e)
{
myLI.Attributes["class"] = "newclass";
}