I have a table that contains a "key" column. The values in this column contain either ID numbers or various "keys" that refer to groups of ID numbers. I want to perform a LookupEx() such that the matching_column argument depends on the value in this key column.

Example 1) The key column contains the value ID123. The LookupEx() function should search for ID123 in column A of table B, and return the value(s) in column C.

Example 2) The key column contains the value SPREAD. The LookupEx() function should search for SPREAD in column D of table B, and return the value(s) in column C.

Since a LookupEx() function cannot be used within an If() function, how might I accomplish this?

Have you tried Tablematch?

I was going to suggest the same thing that @Tony Wong suggested above. A Tablematch may suit your use case, as you can have a key column to match against, and you could then return all of the items in the table that match your key. 

One thing to note is that with a Tablematch, the table used for the formula must have column headers/names that match the column you're searching from in order for it to be found. So if you've called it "Key" in the originating table, then you'll want to call the column you're searching against in the Tablematch table "Key" as well.

Here is a link to the document on Tablematch: https://tbmcouncil.jiveon.com/docs/DOC-5073

Does column A of table B contain the value Spread? If not then it looks like the LookupEx's would be segregated automatically. Alternatively, perhaps you can let the LookupEx's run wild and Filter the combinations that you don't want.

An alternative solution could be to break the problem into separate tables and then combine them once the specific logic has been applied.