You can't apply the regex directly to the lookup command but you can go about this in two different approaches :
1- I think this approach is suitable for the scenario you described here :
| append [|inputlookup enrichment.csv | rex field=user "((?<domain>[^\\\]+)\\\)?(?<user>.+)"]
| stats values(department) as department by host, user
2- Second solution would be to use outputlookup (possibly schedule it) and build the csv file with the right values you require. You can then use that new lookup file without having to worry about regex.
That feature is not currently available. Your best bet is to get the lookup table format corrected (may be split the user field in lookup into domain and user field, so you can match). A workaround could be to create a copy of that lookup (using a regular scheduled search) where you can modify user column to suit your need.