It would definately take you out of ketosis if you ate a sandwich. You would maybe still lose weight as you do in a normal diet, but you would have to go through those first few days of hunger and carb withdrawal again, that's why I've never lapsed
There was a case in America back sometime between 2000 and 2002 (sorry can't be more specific on dates, remember it being on TV when I lived there and was there between those dates), where a guy ate nothing but Subway sandwiches and lost weight. I guess it does all depend on what the filling is. So it is possible, BUT it does go against the LL programme.
You will slip out of ketosis, it won't take you so far out that it will take days to get back in, probably only half a day, that is how you can still lose some weight, but you won't lose what you should as your body has to burn off the sub before it can start burning off fat again.
You would still lose weight having 3 food packs and a sub a day as they aren't that high in cals (it would be like doing the CD 790, although you wouldn't have such high carb content) if you just go for a turkey salad sub with no mayo, they only have around 270 cals, BUT that isn't the point.
The LL programme is about so much more than losing weight, it is about sorting out your head, and you (or whoever) won't do that by eating subs.
One sub will cost you about £70 as you will likely have to stay on LL an extra week to burn it off as well as the cost of the sub.