The problem is that you have an extra "(" in the formula, remove it and error will disapear.
Below three variants of your code, the first variant, in my point of view, is more readable
(in case when you need only values then better to use worksheetfunction)
'==================================================================
'another one variant with same output result
'using worksheetfunction.vlookup (without formulas)
Sub Vlookup_Condition()
Dim Rcnt&, i&, SourceRng$
On Error Resume Next
Application.ScreenUpdating = False
Worksheets("Summary").Activate
SourceRng = Range("A:B").Address
With Worksheets("Summary")
Rcnt = .Cells(Rows.Count, 1).End(xlUp).Row
For i = 2 To Rcnt
.Cells(i, 3).Value = WorksheetFunction.VLookup(.Cells(i, 1).Value, _
Worksheets("FinancePartnerList").Range(SourceRng), 2, 0)
If Err.Number > 0 Then
.Cells(i, 3).Value = "Not in Exception List": Err.Clear
End If
Next
End With
Application.ScreenUpdating = True
End Sub
'==================================================================
'your updated variant
'using formulas
Sub Vlookup_Condition_Formula1()
Dim Rcnt&, i&
Application.ScreenUpdating = False
Worksheets("Summary").Activate
With Worksheets("Summary")
Rcnt = Cells(.Rows.Count, 1).End(xlUp).Row
For i = 2 To Rcnt
Cells(i, 3).Formula = "=IFERROR(VLookup(" & .Cells(i, 1).Address _
& "," & "'" & Sheets("FinancePartnerList").Name & _
"'!A:B," & "2, 0), ""Not in Exception List"")"
Next
End With
Application.ScreenUpdating = True
End Sub
'==================================================================
'your updated variant
'using Evaluate(formulas)
Sub Vlookup_Condition_2()
Dim Rcnt&, i&
Application.ScreenUpdating = False
Worksheets("Summary").Activate
With Worksheets("Summary")
Rcnt = Cells(.Rows.Count, 1).End(xlUp).Row
For i = 2 To Rcnt
Cells(i, 3).Value = Evaluate("=IFERROR(VLookup(" & .Cells(i, 1).Address _
& "," & "'" & Sheets("FinancePartnerList").Name & _
"'!A:B," & "2, 0), ""Not in Exception List"")")
Next
End With
Application.ScreenUpdating = True
End Sub