Here’s one approach. First group into lists and then process the lists into the values you actually want:
import static java.util.Comparator.comparingLong;
import static java.util.stream.Collectors.groupingBy;
import static java.util.stream.Collectors.toMap;
Map<Route,Integer> routeCounts = routes.stream()
.collect(groupingBy(x -> x))
.values().stream()
.collect(toMap(
lst -> lst.stream().max(comparingLong(Route::getLastUpdated)).get(),
List::size
));