Hi I'm looking for an Ito-type lemma for rough paths but am having difficulty finding something. Could someone kindly point me in the right direction?
In addition to what Nate Eldredge mentioned, here is a recent paper that you might like to consider.
Keller, Christian; Zhang, Jianfeng Pathwise Itô calculus for rough paths and rough PDEs with path dependent coefficients. Stochastic Process. Appl. 126 (2016), no. 3, 735–766.
This copy is publicly available at the arXiv.