PHP 503 errors are generally PHP crash errors. Please note, this is not a LiteSpeed Web Server error.
If you are using a control panel such as cPanel, you will most likely experience the same error when temporarily switching to Apache. Troubleshooting PHP errors is generally out of our support scope.
However, we do provide a comprehensive guide for you to use in troubleshooting the errors yourself. We use the same guide to internally troubleshoot 503 errors as well .
This includes checking logs, disabling the opcode cache for PHP, increasing PHP memory, changing PHP versions, disabling unsafe extensions, checking disk space, checking LVE memory limits, checking LVE process limits, etc.
If you are overwhelmed by the steps in the troubleshooting guide, you may engage us through our hourly support. We will troubleshoot on your behalf and try our best to fix the issue for you.
Please order our hourly premium support service. Then, provide a temporary root password to your server and detailed steps to reproduce the issue in the support ticket.
If a 503 error only occurs while using LiteSpeed, not with Apache, then please log a bug report so that we may investigate further.