I used the LocalDate class as well. I think I have a working solution. First I find the number of years between the two dates using the birthDate.until(deathDate, ChronoUnity.YEARS); Then, I add the number of years to the original birthDate. Then I find the difference in days between the new date and the deathDate. Here is a snipet of my code (where birthDate and deathDate are LocalDate objects:
long ageInYears = birthDate.until(deathDate, ChronoUnit.YEARS);
birthDate = birthDate.plusYears(ageInYears);
long leftoverDays = birthDate.until(deathDate, ChronoUnit.DAYS);
Note: my code checks to ensure the birthDate is before the deathDate, not sure if that matters. I think it would just make the age negative.