Replicators such as parasites invading a new host species, species invading a new ecological niche, or cancer cells invading a new tissue often must mutate to adapt to a new environment. It is often argued that a higher mutation rate will favor evolutionary invasion and escape from extinction. However, most mutations are deleterious, and even lethal. We study the probability that the lineage will survive and invade successfully as a function of the mutation rate when both the initial strain and an adaptive mutant strain are threatened by lethal mutations. We show that mutations are beneficial, i.e. a non-zero mutation rate increases survival compared to the limit of no mutations, if in the no-mutation limit the survival probability of the initial strain is smaller than the average survival probability of the strains which are one mutation away. The mutation rate that maximizes survival depends on the characteristics of both the initial strain and the adaptive mutant, but if one strain is closer to the threshold governing survival then its properties will have greater influence. These conclusions are robust for more realistic or mechanistic depictions of the fitness landscapes such as a more detailed viral life history, or non-lethal deleterious mutations.