I know that LookupColumns use the format {0};#{1} where {0} is the ID of the
lookup item and {1} is the Text of the Lookup Item. So I tried doing a
SELECT CASE on the AssignTo and making the sAssignTo contain the ID and the
Text; e.g.

Case "Robert Filipiak"
sAssignTo = "2;#Robert Filipiak"

That didn't work either. I tried:

newItem("Assigned To") = SharePointWeb.Users(sAssignTo)

That didn't work either but the new list item got created without the
anything in the 'Assigned To' column.

That got me thinking and I went back to using

newItem("Assigned To") = sAssignTo

but change the SELECT CASE to:

Case "Robert Filipiak"
sAssignTo = "2"