You can suppress the *display* of zeroes by unticking Tools | Options... | LibreOffice Calc | View | Display | Zero values, but this change does not seem to carry over into the printed result, so won't help you. One way I can see is the obvious one: to construct your formulae appropriately.
If there is no entry, say, in A6 and you want a related formula not to show zero, you need to change
=expression
to something like
=IF(expression<>0;expression;"")
or
=IF(A6<>0;expression;"")
or
=IF(A6<>"";expression;"")
as appropriate.
But here's another idea. You can create formats that handle different ranges of values differently. To get the idea, go to Format | Cells... | Numbers | Currency and look at the formats as expressed in the "Format code" box. (You may well be using currency formats for invoices anyway.) You should find that at least some of the formats have different expressions for positive and negative values, separated by a semicolon. If you add another semicolon at the end, you can also set a format for zero values, and if you use # or "" for this extra format, zero values will display as nothing. Such changes will carry across into the printed output, of course.
I trust this helps.
Brian Barker