HI Lisa- you ask an excellent question. 
– Shingrix is non-live, recombinant vaccine just recently approved for prevention of zoster.
– Zostavax is a live, attenuated vaccine approved for prevention of zoster. 
Given the recommendation to avoid live vaccines while on immunotherapy, Shingrix would be the better of the two choices.  Agreed- we do not have data regarding safety of use in the setting of immune therapy, specifically immune checkpoint inhibitors, but theoretically….. 
This may be an ideal option for patients at risk; and importantly, prevention of zoster prevents associated post-herpetic neuralgia—this is debilitating for some individuals.  
Thanks for posing this question Lisa.