Please refer to these documents to optimize your LiteSpeed performance:
In our experience, generally speaking, these are the most possible logical explanations:
Your PHP setup may be different among your systems. Please verify. Try to turn on PHP opcode cache.
MySQL might be the cause as well. Please check with the Top command output. If your PHP process uses a lot of CPU resource, the bottleneck is the PHP code. If MySQL uses a lot of CPU resource, then your issue is caused by MySQL. Perhaps a table needs to be indexed.
Lastly, if the CPU usage is not high, you may have some network bottleneck. It could be a failure in the DNS lookup or a script has slow speed accessing another server.