At lease some lounge provision has been made, many European stations have noting, even when lounges are available to other airlines. T1 Escape to T3 is quite a hike - I can’t remember how get to T3 from T1, is it by turning left just before the walk-through duty free shop? The airside route has been closed for years, since Security at T1 was moved.
I imagine there will be some sort of branded lounge situation at T2, as you say. It could be BA branded and operated by a third party, which happens or might have one world/EI branding. EI are in an unusual situation, they are part of the one world JV, but not the alliance. Talk about confusing for customers.