Neither Etihad not Alitalia has their own lounge in Bangkok. [If either Alitalia or Etihad had their own lounge in BKK, then of course you would have entry]
Therefore, you are in a "third party lounge" situation.
Etihad contracts the Thai Royal Orchid Lounge in Bangkok. This covers passengers in First/Business on Etihad flights, and Economy passengers having the requisite status in the Etihad Guest programme only.
Alitalia does not have any contract with any lounge provider in BKK - so your Millemiglia status does not get you any lounge access.
airberlin does not have any contract with any lounge provider in BKK - so your topbonus status does not get you any lounge access.