Grouping by and map value

You need to chain a Collectors.mapping() collector to the Collectors.groupingBy() collector:

Map<String, List<Fizz>> collect =
    docs.stream()
        .collect(Collectors.groupingBy(DistrictDocument::getCity,
                 Collectors.mapping(d->createFizz(d),Collectors.toList())));

If createFizz(d) would return a List<Fizz, you can flatten it using Java 9’s Collectors.flatMapping:

Map<String, List<Fizz>> collect =
    docs.stream()
        .collect(Collectors.groupingBy(DistrictDocument::getCity,
                 Collectors.flatMapping(d->createFizz(d).stream(),Collectors.toList())));

If you can’t use Java 9, perhaps using Collectors.toMap will help:

Map<String, List<Fizz>> collect =
    docs.stream()
        .collect(Collectors.toMap(DistrictDocument::getCity,
                                  d->createFizz(d),
                                  (l1,l2)->{l1.addAll(l2);return l1;}));