How can I manually set the LFE volume in Premiere's "Audio Track Mixer" panel?
I understand, that by saying "manually" you mean: input digits with keyboard.

There is no easy way to manipulate this exact setting that way through UI - if you want more precise control hold Ctrl while click dragging the slider your mouse left-right.

However if you really need to be on the exact number (and perhaps you will set this once for entire project) - there is a hack, that will allow you to set this value to exact number:


Make backup of your project before doing any changes this way.
Close the project in Premiere if you have it open.
Open your .prproj file with zip archive tool (like 7-Zip), inside you will find xml file representing all settings of the project.
Open it with a text editor - I recommend Atom or something with syntax highlighting.
Search for "LFE", edit appropriately (this may require some educated guesses).
Put xml file back into archive, and re-open in Premiere.


Good luck!