  We show existence and uniqueness of solutions of stochastic path-dependent
differential equations driven by cadlag martingale noise under joint local
monotonicity and coercivity assumptions on the coefficients with a bound in
terms of the supremum norm. In this set-up, the usual proof using the ordinary
Gronwall lemma together with the Burkholder-Davis-Gundy inequality seems
impossible. In order to solve this problem, we prove a new and quite general
stochastic Gronwall lemma for cadlag martingales using Lenglart's inequality.
