In Java 8 how do I transform a Map<K,V> to another Map<K,V> using a lambda?

You could use a Collector:

import java.util.*;
import java.util.stream.Collectors;

public class Defensive {

  public static void main(String[] args) {
    Map<String, Column> original = new HashMap<>();
    original.put("foo", new Column());
    original.put("bar", new Column());

    Map<String, Column> copy = original.entrySet()
        .stream()
        .collect(Collectors.toMap(Map.Entry::getKey,
                                  e -> new Column(e.getValue())));

    System.out.println(original);
    System.out.println(copy);
  }

  static class Column {
    public Column() {}
    public Column(Column c) {}
  }
}

Map<String, Integer> map = new HashMap<>();
map.put("test1", 1);
map.put("test2", 2);

Map<String, Integer> map2 = new HashMap<>();
map.forEach(map2::put);

System.out.println("map: " + map);
System.out.println("map2: " + map2);
// Output:
// map:  {test2=2, test1=1}
// map2: {test2=2, test1=1}

You can use the forEach method to do what you want.

What you're doing there is:

map.forEach(new BiConsumer<String, Integer>() {
    @Override
    public void accept(String s, Integer integer) {
        map2.put(s, integer);     
    }
});

Which we can simplify into a lambda:

map.forEach((s, integer) ->  map2.put(s, integer));

And because we're just calling an existing method we can use a method reference, which gives us:

map.forEach(map2::put);

The way without re-inserting all entries into the new map should be the fastest it won't because HashMap.clone internally performs rehash as well.

Map<String, Column> newColumnMap = originalColumnMap.clone();
newColumnMap.replaceAll((s, c) -> new Column(c));