If you want lounge access for domestic flights in the U.S. on AA/AS, you would need oneworld Sapphire or Emerald in a non-U.S. oneworld FFP. BAEC/Iberia Plus seem the likely candidates for you. And oneworld Sapphire or Emerald with BAEC or IB+ would also get you Main Cabin Extra seats at time of booking on AA.

But if you're looking for free class upgrades on AA or AS, you would need elite status in either one of those programs. That said, if you'd only be able to attain relatively low-level status with AA or AS, you might find that your upgrade percentage would be relatively low.

Edited to add: For Business Class roundtrips from TLV to U.S. West Coast, you would likely achieve oneworld status faster by crediting to BA, as long as you were able to fly the minimum number of BA flight segments. In fact, you could attain OWS status after just one roundtrip if you included one domestic segment on AA or AS. For example: LHR-TLV-JFK-LAX, or TLV-LHR-SFO-SEA.