I'm afraid not .. Aer Lingus isn't a oneworld member so the BAEC relationship is confined to flights where they codeshare (principally Heathrow flights to/from Ireland)

So you won't be able to access the lounge in Dublin if you're departing to FRA as there's no BA codeshare .. and in FRA i don't know what lounge EI use but you won't have any access I'm afraid (Even if you're BA Gold there's no BA lounge in FRA I dont' think .. they use the JAL Lounge ... so no Gold open doors access I'm afraid)