There the situation as far as I know was that they got the slots and then we're takeover by Ryanair. Initial coordinator was with condor and eurowings but those very quickly fell away as Ryanair came in to basically do a takeover before they even started service.
So there was a moment where they were an independent 3rd party airline for the purposes of assigning slots. If that was the plan from the start who knows. The business plan of Lauda did change drastically after Ryanair came in.
To the initial questions. Ocean would just count as LH under a different name as it a fully owned subsidiary. I would imagine that it wouldn't be the new competitor they were looking for.