Note: LiteSpeed WordPress Cache plugin needs to be v1.3+.

Let's take **Caldera Forms Version 1.5.6.1** as the example. 

In <code>caldera-forms/classes/render/nonce.php</code> line 86 <code php>public static function nonce_field( $form_id )</code> is where the form nonce is generated. So to convert it to ESI, change
<code php>
	public static function nonce_field( $form_id ){
		$nonce_field = '<input type="hidden" id="' . esc_attr( self::nonce_field_name( $form_id ) ) . '" name="' . esc_attr( self::nonce_field_name() ) . '" value="' . esc_attr( self::create_verify_nonce( $form_id ) ) . '"  data-nonce-time="' . esc_attr( time() ) . '" />';
		$nonce_field .= wp_referer_field( false );
		return $nonce_field;
	}
</code>

to

<code php>
	public static function nonce_field( $form_id, $from_esi = false ){

		if ( ! $from_esi ) {
			if ( method_exists( 'LiteSpeed_Cache_API', 'esi_enabled' ) && LiteSpeed_Cache_API::esi_enabled() ) {
				if ( method_exists( 'LiteSpeed_Cache_API', 'v' ) && LiteSpeed_Cache_API::v( '1.3' ) ) {
					$params = array( 'form_id' => $form_id ) ;
					return LiteSpeed_Cache_API::esi_url( 'caldera_forms', 'Caldera Forms', $params ) ;
				}
			}
		}

		$nonce_field = '<input type="hidden" id="' . esc_attr( self::nonce_field_name( $form_id ) ) . '" name="' . esc_attr( self::nonce_field_name() ) . '" value="' . esc_attr( self::create_verify_nonce( $form_id ) ) . '"  data-nonce-time="' . esc_attr( time() ) . '" />';
		$nonce_field .= wp_referer_field( false );
		return $nonce_field;
	}

	/**
	 * Handle ESI request
	 *
	 */
	public static function hook_esi( $params ) {
		$form_id = $params[ 'form_id' ] ;
		echo self::nonce_field( $form_id, true ) ;
		exit ;
	}
</code>

Then go to <code>caldera-forms/classes/core.php</code>, in <code php>function __construct()</code> line 146 or other preferred position, add this:
<code php>
		if ( method_exists( 'LiteSpeed_Cache_API', 'esi_enabled' ) && LiteSpeed_Cache_API::esi_enabled() ) {
			LiteSpeed_Cache_API::hook_tpl_esi( 'caldera_forms', 'Caldera_Forms_Render_Nonce::hook_esi' );
		}

</code>

Now **Caldera Forms** can be perfectly cached with ESI on.