That's why we recommend keeping PHP for Apache and LiteSpeed in sync. When you upgrade PHP, upgrade Apache first, then LiteSpeed.
If you want to the easiest soltuion, just "Build Matching PHP" from our WHM plugin.
Or, you need to setup LiteSpeed PHP completely independent to Apache PHP, build LSPHP through admin console and install it to $SERVER_ROOT/lsphp5, so it will use a different php.ini file.
To use a different php.ini without rebuild PHP, you can add a command line parameter to lsphp5 external application like ".../lsphp5 -c <path_to_php.ini>"