RFR's will be compounded in-arrears, if I have an option on this rate am I forced to use Monte Carlo or are there techniques in the literature that will price path-dependent trades with a backwards pricing method (PDE/lattice etc)?
Yes you can price Asian-style options in PDEs, by introducing an extra state variable which is the accumulated Asian variable (in your case the RFR rate). It is well covered in literature, a quick Google search on "pricing Asian options in PDE" should bring plenty of results. For example this, equation (3) shows the PDE to solve. Notwithstanding your comment, for caplets on RFR rates in the Hull-White model there are closed-form solutions.