Removes the ul wrapper on any sub-menus beyond the 2nd level.

limit-sub-menu-level-wp.php

<?php
/**
 * Limit the number of sub-menu levels outputted.
 *
 * Removes the ul wrapper on any sub-menus beyond the 2nd level.
 * 
 * @author Joshua David Nelson, josh@joshuadnelson.com
 */
// Add menu walker to primary menu
add_filter( 'wp_nav_menu_args', 'jdn_primary_menu_args' );
function jdn_primary_menu_args( $args ) {
 
	if( isset( $args['theme_location'] ) && 'primary' == $args['theme_location'] ) { // change based on the location
		$walker = new JDN_Primary_Nav_Walker;
		$args['walker'] = $walker;
	}
 
	return $args;

}

// Custom Walker
class JDN_Primary_Nav_Walker extends Walker_Nav_Menu {
	
	function start_el( &$output, $item, $depth = 0, $args = array(), $id = 0 ) {
		// Remove 'menu-item-has-children' class from elements beyond the second depth level
		if( $depth > 1 && isset( $item->classes ) && is_array( $item->classes ) && ( $key = array_search( 'menu-item-has-children', $item->classes ) ) !== false ) {
			unset( $item->classes[ $key ] );
		}
		parent::start_el( $output, $item, $depth, $args );
	}
	
	// Starting of a sub-menu
	function start_lvl( &$output, $depth = 0, $args = array() ) {
		$indent = str_repeat("\t", $depth);
		if( $depth < 2 ) {
			$output .= "\n$indent<ul class='sub-menu'>\n"; // The default wrap
		} elseif( $depth >= 2 ) {
			$output .= "\n$indent\n"; // no sub menu wrap
		}
	}
	
	// End of a sub-menu
	function end_lvl( &$output, $depth = 0, $args = array() ) {
		$indent = str_repeat("\t", $depth);
		if( $depth < 2 ) {
			$output .= "$indent</ul>\n"; // the default wrap end
		} elseif( $depth >= 2 ) {
			$output .= "\n$indent\n"; // no wrap
		}
	}
}