The article linked in the first post suggests that this new fare would not even include hand luggage.
In Spain, courts have repeatedly held that Spanish and EU law/Directive not only include "cabin baggage", but that "cabin baggage" includes anything that should comfortably fit - including in the overhead bins - based on the size/shape of the aircraft, and that airlines' charges to carry on a full/normal sized carry on bag (that is, which has to go in the overhead bin) violated the law.
The airlines of course are trying to challenge this at the EU level, but there is also an EU court decision which seems to side with the Spanish.
In any case, EU rules I believe - and in any case, with certainty, Spanish written law and court cases - would not allow a no-cabin-baggage-at-all fare, as the article seems to suggest that LH is considering.
(n.b. there were a bunch of articles a year or so ago that got ahead of reality, announcing "new EU rules"; the EC never agreed on it, and the rules at the EU level did not change). [See https://www.euronews.com/my-europe/2...ers-rights-law - this was a good thing, because the drafted rule would have set a uniform standard much lower than that which major airlines currently allow; I apologize, I know the Spanish courts and EU courts have spoken about EU rules on the matter, but I cannot find the specific reference at the moment].