In this work, we study the problem of unconstrained convex optimization in a fully distributed multiagent setting, which includes asynchronous computation and lossy communication. In particular, we extend a recently proposed algorithm named Newton-Raphson consensus by integrating it with a broadcast-based average consensus algorithm, which is robust to packet losses. We show via the separation of time-scale principle that under mild conditions (i.e., persistency of the agents activation and bounded consecutive communication failures), the proposed algorithm is provably locally exponentially stable with respect to the optimal global solution. Finally, we complement the theoretical analysis with numerical simulations and comparisons based on real datasets.