If the date of birth is stored in the last name property (which is a strange choice), the filtering should be as follows:
List<String> filteredLst = someHashMap.entrySet().stream()
.filter(e -> list.stream()
.map(p->p.getPerson().getLastName())
.anyMatch(lastname -> lastname.equals(e.getKey())))
.map(Map.Entry::getValue)
.collect(Collectors.toList());
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