I don't know if this will help you or not, but just some observations I've made. When I first started this game I was on a beat up, old 4s. Seemed to have the same lag as everybody. Then there was the "bad" time, where it got so bad that I couldn't play at all. That was programming, and once that got fixed it was a lot better. I still had to have everything but chat turned off, since that would increase the lag dramatically. In late February I finally got a 5s. It was great! Everything worked, and best of all, no lag with everything turned on. As time went on I began to notice that the lag problems started to crop up again, so I tried deleting old text messages and saving pictures to the cloud. Surprisingly, this seemed to solve the problem.
We were just in a game and you had to leave because you were lagging so badly. We are on similar devices and I wasn't lagging at all. I don't know if anything that I've said is helpful to you, but I hope so. It was a good game and I was sorry to see you leave.
All the best, Fluffy