You may do this by adding the following CSS styles to your webpage:
top: 125px !important;
top: 115px !important;
Just change both (top:) numbers to desired values to move the tab lower or higher on the webpage.
*To keep the Tab and the Help Panel inline with each other, please make sure that your .lhn_help_btn top position is 10 pixels higher than the .lhn_help_container top position.
There are a variety of other ways to customize the HelpOut Tab: