In a lookup enricher is there a way to tell: 'Do nothing' in fallback value because my output will be NULL instead of a previous value? Also what are the limits of the SQL Custom parameter that would make the enricher not work ? Thanks in advance

The options for Behavior on Error include skips the current record, skips the entire task, or stops the whole job.

If you want to know if you can put any custom Sql query as complex as it is with LOOKUP_COLUM and output_column1, then the answer is yes, you should be able to use any custom function in the Lookup_Column