As a general rule, US-based carriers do not allow their own elites access to lounges when travelling on "domestic" (non-international) itineraries (their definition of domestic/non-international generally means flights within the US, between US and Canada, and between US and some Caribbean countries).
This restriction only applies to their own members (e.g. it would apply to DL SkyMiles & CO OnePass members, but it would not apply to OK Plus or AF F+ members).
The same rule is also applicable for the *A and OneWorld lounge access...