Are the Turkish places on Green Lanes open Sundays?
Yes, particularly the stretch down toward Haringay/Green Lanes Station - even on a Sunday that area is mostly open and busy, particularly from lunch into the afternoon - this is because it's right by a shopping park. If I was looking for good Turkish food (and a variety of it) I'd start in this area, rather than the stretch between Turnpike Lane and Wood Green, which tends to have more fried chicken and coffee chains.
Ended up going a bit further South, to the cluster just north of Dalston Kingsland rail, thanks to the train to Green Lanes being down.
I can report that about two thirds of the cluster of Turkish places just north of the station were open for Sunday lunch, but most seemed to be offering a restricted menu - I don't think many/any were barbecuing that day, but there were several places turning out fresh-made gozleme and manti, which is what I'd recommend having in similar circumstances.
The pre-made meat dishes were ok, but nothing special.