Whenever you attempt to print to a printer that does not exist (you must use SET PRINTER TO NAME in VFP) then VFP will print to the windows default printer.
You must have a valid windows printer name on the machine that you are printing to, even in Windows 98.
For Windows 98, make sure the printer share name is 8 characters or less for your test. Then test the below:

lcorgprinter = SET('PRINTER',3)  && default VFP printer
lcprinter = GETPRINTER()         && select the Zebra printer here
SET PRINTER TO NAME (lcprinter)
*Print the labels then set the printer back
SET PRINTER TO NAME (lcorgprinter)

If that works, then there must be a difference between the actual printer name in Windows 98 and the one stored in Our_Label_PrinterName_Parameter.

>VFP 8.0 SP1
>We want to switch printers after an invoice print (Dot Matrix) so we can print some labels on a Zebra Label Printer. It all works well in WinXp & 2000 but not Win98 and unfortunately our customers won't upgrade for a while yet. The following code works in XP & 2000.
>
>Set Printer To Name (Our_Label_PrinterName_Parameter)
>
>So instead we are trying the DOS "Net Use" command before we print to capture the port and re-direct it to the Zebra Network Printer.
>
>Set Printer To LPT3 (which we have already captured) always prints on the windows default printer and does not go out to the Captured Printer. The strange thing about this is issuing the Set Printer To LPT3 in Fox for DOS works fine, any suggestions.