Updates URLs on susbites and in lost password request emails to point to the subsite where the lost password request started.

subsite-lostpassword.php

<?php
/*
Plugin Name: Subsite Lostpassword
Plugin URI: http://www.paidmembershipspro.com/wp/subsite-lostpassword/
Description: Updates URLs on susbites and in lost password request emails to point to the subsite where the lost password request started.
Version: .1
Author: Stranger Studios
Author URI: http://www.strangerstudios.com
*/
/*
	Fixes the URL at the bottom of the login page.
*/
function sslp_lostpassword_url($url, $redirect)
{	
	$args = array( 'action' => 'lostpassword' );
	if ( !empty($redirect) ) {
		$args['redirect_to'] = $redirect;
	}

	$lostpassword_url = add_query_arg( $args, site_url('wp-login.php', 'login') );
	return apply_filters( 'lostpassword_url', $lostpassword_url, $redirect );
}
add_filter("lostpassword_url", "sslp_lostpassword_url", 10, 2);

/*
	Fixes URL in email that goes out.
*/
function sslp_retrieve_password_message($message, $key)
{
	if ( empty( $_POST['user_login'] ) ) {
		return $message;	//error probably
	} else if ( strpos( $_POST['user_login'], '@' ) ) {
		$user_data = get_user_by( 'email', trim( $_POST['user_login'] ) );
		if ( empty( $user_data ) )
			return $message;	//another error condition, no user found
	} else {
		$login = trim($_POST['user_login']);
		$user_data = get_user_by('login', $login);
	}
	
	$user_login = $user_data->user_login;
	
	$message = __('Someone requested that the password be reset for the following account:') . "\r\n\r\n";
	$message .= home_url( '/' ) . "\r\n\r\n";
	$message .= sprintf(__('Username: %s'), $user_login) . "\r\n\r\n";
	$message .= __('If this was a mistake, just ignore this email and nothing will happen.') . "\r\n\r\n";
	$message .= __('To reset your password, visit the following address:') . "\r\n\r\n";
	$message .= '<' . site_url("wp-login.php?action=rp&key=$key&login=" . rawurlencode($user_login), 'login') . ">\r\n";
	
	return $message;
}
add_filter("retrieve_password_message", "sslp_retrieve_password_message", 10, 2);

I'm seeing the same error as shiyam06 with

Premature end of script headers

in the error log.

To fix this problem, replace like 20 and 21 with:

$lostpassword_url = add_query_arg( $args, site_url('wp-login.php') );
return apply_filters( 'lostpassword_url', $lostpassword_url, $redirect );

I would suggest replacing this in the code itself strangerstudios. It fixes the Internal Server Error (which throws a 520 Unknown Error if you have cloudflare on. Took me some time and good debugging skills to figured this one out).

This seems to not be working in the latest version of Wordpress (multisite)

I wrote my own implementation, if anyone still needs it: https://gist.github.com/eteubert/293e07a49f56f300ddbb