Add function to custom menu

Simple, don’t bundle the function inside. Instead, break it out like this:

//--Nav Menu
function add_profile_link_to_nav(){ 
    if ( is_user_logged_in() ) { ?> 

<ul> 
    <li class="menu-item"id="one"> <a href="http://example.com/members/">All  Members</a>
        <ul class="sub-menu"> 
            <?php echo custom_execute_shortcode(); ?>
            <li class="menu-item"> </li>
        </ul> 
    </li>
</ul>    <!--end menu--->
    <?php } 
}
add_action( "wp_nav_items","add_profile_link_to_nav" );

function custom_execute_shortcode() {
     $myfunction= '[Shortcode]';
     $myfunction_parsed = do_shortcode($myfunction);
     return $myfunction_parsed;
}