Okay thank you. Let's try the following troubleshooting steps first.
1. Check the server requirements for Toolset and make sure your server meets those requirements, specifically the mbstring module, suhosin, and eval function settings: https://toolset.com/toolset-requirements/
2. Temporarily deactivate all plugins except Types, Views, and Layouts. Activate a default theme like Twenty Seventeen. If you want, you can activate a Maintenance Mode plugin during testing.
3. Try to save a Layout. If the problem is resolved, reactivate your theme and other plugins one by one until the problem returns. If the problem was not resolved, continue.
4. Try bumping up the available memory by adding these two lines to your wp-config.php file, just before it says "That's all, stop editing!"
define('WP_MEMORY_LIMIT', '512M');
define( 'WP_MAX_MEMORY_LIMIT', '512M' );
5. If increasing the available memory does not solve the problem, turn on server error logs to see if anything is registered. To do that, go in your wp-config.php file and look for
define('WP_DEBUG', false);
Change it to:
define('WP_DEBUG', true);
Then add these lines, just before it says 'stop editing here':
ini_set('log_errors',TRUE);
ini_set('error_reporting', E_ALL);
ini_set('error_log', dirname(__FILE__) . '/error_log.txt');
Trigger the 503 error once more, then look for an error_log.txt file in your site's root directory. Please send me its contents. Once that is done, you can revert the changes you made to wp-config.php.
If you do not find an error log file, and none of the other troubleshooting steps worked, I'll need to take a closer look.