Answer
By default a Custom LU's key is OBJKEY, but OBJKEY is a system-generated GUID that has no source-data equivalent for the migration job to map to, so an update job has nothing to match against. In Source Mapping, remove the Key (K) flag from OBJKEY and mark it as an Ignore-on-update (I) column instead, then flag whichever source-mapped business column(s) should uniquely identify a record as the Key(s) instead, keeping them in sequential order. In Method List Attributes, make sure Column Sequence and the On New / On Modify flags are kept consistent with whatever you changed in Source Mapping. The migration job then uses those business-column Alternate Keys to look up the correct OBJKEY internally instead of expecting it directly from the source data.