After WP Plugin update Hook

after_wp_updates.php

/**
* Purge LiteSpeed Cache after updates. 
*
* This snippet will check if LS plugin is activated & then Purge all Cache 
* after any Core, Theme or Plugin Installation, Update or rollback. Then it 
* will email the results to the given address on line 35. Disable by commenting out 
* line 39.
*
* @howto: Update line 35 with your email address and save the code snippet to Execute on Child Sites.
*
* @snippetType: Execute on Child Sites
*/
function my_upgrade_function( $upgrader_object, $options ) {
	$purged = 'has not been purged.';

	// Purge all LS Cache. 
	if ( defined( 'LSCWP_V' )) {
		do_action( 'litespeed_purge_all' );
		$purged = 'has been purged.';
    	}

	// Grab Admin Notices.
	ob_start(); // start capturing output.
	do_action( 'admin_notices' );
	$admin_notice_output = ob_get_contents(); // the actions output will now be stored in the variable as a string!
	ob_end_clean(); // never forget this or you will keep capturing output.

	// Grab Site Name.
    	$site_name = get_bloginfo('name');

	// Build Email.
	$email_subject = 'Notification: ' . $site_name . ' status has changed.';
	$email_body = 'The child site ' . $site_name . ' ' . $purged . '.<br>
			The current Admin Notices are as follows:<br><br>' . $admin_notice_output;

	// Set Email Headers.
	$to = 'YOU_EMAIL@email.com';
	$subject = $email_subject;
	$body = $email_body;
	$headers = array('Content-Type: text/html; charset=UTF-8');
	
	// Send Email. 
	wp_mail( $to, $subject, $body, $headers );
}
add_action( 'upgrader_process_complete', 'my_upgrade_function',10, 2);