Carl
Have you looked at the documentation for LHE? You can see docs for many tools by clicking on the browse document button on the tool. Here it is for LHE and the tool does not work in the way you are thinking. For that you may want to look at GradientHDRCompression. At the end of the documentation in the Usage Hints section 2.2 this tool is experimental 8) which I take at results may be surprising,haha.
Mike