There is no general answer. But, you should presume strict enforcement, most especially by LH. *A carriers invoice the "home" carrier, SK in your case, for the use of their lounge. If LH staff admit you and too many guests to its lounge and try to invoice SK and SK does not pay the extra fee, the lounge staff at FRA will hear about it from their employer.
There is no harm in asking, but you should be pleased if allowed and accepting if not.