196. Throwing checked exceptions from lambdas

Let's suppose that we have the following lambda:

static void readFiles(List<Path> paths) {
  paths.forEach(p -> {
    try {
      readFile(p);
    } catch (IOException e) {
      ... // what can we throw here?
    }
  });
}

What can we throw in the catch block? Everybody knows the answer … we can throw an unchecked exception such as RuntimeException:

static void readFiles(List<Path> paths) {
  paths.forEach(p -> {
    try {
      readFile(p);
    } catch (IOException e) {
      throw new RuntimeException(e);
    }
  });
}

Also, everybody knows that we cannot throw a checked exception such as IOException. The following snippet of code will not compile:

static void readFiles(List<Path> paths) {
  paths.forEach(p -> {
    try {
      readFile(p);
    } catch (IOException e) {
      throw new IOException(e);
    }
  });
}

Can we change this rule? Can we come up with a hack that allows us to throw checked...