check domlogs (e.g. /usr/local/apache/domlogs/domain). if they are not growing, do one of the followings:
1. Do force-reinstall lsws from WHM Plugins -> LiteSpeed Web Server -> Admin Web Console (Actions -> Version Manager )
or
2. Download lsws package and re-install from command line. Use 'U'pgrade option to keep your existing configurations.