Lets first understand the profile and lookup datasets and their intent.
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Profile datasets (person-centric, merged into the Unified Profile store and viewable in Profile Viewer), and
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Lookup / relationship (“dimension”) datasets (reference entities used at segmentation time or journey runtime, not materialized into the person profile record you browse in the UI).
Adobe’s Profile store is not a relational store. Adobe supports “multi-entity segmentation” by linking small “dimension entities” (lookup entities) to the primary person entity via relationships, but that doesn’t mean the lookup columns get copied onto the person profile and shown in Profile Viewer. Even if the lookup dataset is profile-enabled, Profile is not a relational store, so you typically won’t see lookup attributes on the person profile.
Adobe recommends using a non-person identifier as the primary identity of a lookup schema because lookup keys are intended to represent reference entities (productId, storeId, offerId, etc.), not people. If a person identifier (email/ECID/CRMID) is used as the primary identity on a lookup dataset, it can have unintended Identity Service/Profile side effects (identity graph pollution, unexpected merges, governance implications) and can be operationally fragile if duplicate keys occur.
If the dataset is truly person enrichment (additional CRM/profile attributes), the recommended pattern is to ingest it as an XDM Individual Profile dataset (profile schema) rather than a lookup entity, so the attributes become part of the unified profile and can be viewed/used normally.