QE2 deck plans portray the F Stairway lift doors opening forward on 1 and 2 Decks. Given your photos, personal account and my memory, there is only one lift landing for both of these decks which is the one shown in your photo and it clearly opens aft.
I don't recall this lift having a fore and aft door arrangement so perhaps the printer got it wrong or the deck plans are showing a crew lift by mistake?