VBA Function slower than Excel Formula
I'm assuming that names have been changed to protect the innocent, but just in case they've not been...

These are terrible names. All of them.


Function names should have verb-noun names and be PascalCased. So instead of CUSTOMFUNCTION should be GetCustomMatch (or something like that. I can't say because you've ommitted any actual names...)
Parameters should be camelCase and tell me what kind of data
should be passed in and NEVER should they be numbered the way
this is. So, maybe this instead (again, I have to guess because I
have no clue):

Function GetCustomMatch(LookupRange As Range, lastYearsSalesRange as Range, iJustDontKnowWhatThisIsRange as Range) As String

Don't use hungarian notation. Just... please don't. It should be
killed with fire and buried out back.




Other Stuff


Some of your "Values" are used in multiple places. Store them in a
constant and use that constant anywhere they show up. (Of course,
use meaningful names for them.)
I have a feeling that sTableMatchingFieldLookup and ...Result should be actual ranges instead of strings. String typing is bad. If you insist on keeping them as strings, store the values as constants. 
You should be able to pick up some performance by setting Application.Calculation = xlCalculationManual. This Stack Overflow answer has a pretty good example of what you're trying to do.


Things you did right


You exit early if you've already found a match before performing the lookup rather than nesting if statements.