As you have discovered, filtering on a lookup of a single/multiple select does not work the same as with the original field.
One workaround is to create a new formula field based on the lookup, and then perform the filter on the formula field.
Formulas based on lookup fields can get a little tricky, and often require manually converting the lookup field value to a string: {lookup field} & ""
. You will also need a combination of IF
, and FIND
functions. They are documented in the formula field reference.