WordPress Multisite: Password Reset on a Subsite.

functions.php

/**
 * Password reset on sub site (1 of 4)
 * Replace login page "Lost Password?" urls.
 *
 * @param string $lostpassword_url The URL for retrieving a lost password.
 * @param string $redirect The path to redirect to.
 *
 * @return string
 *
 * @since 1.0.0
 */
function custom_lostpassword_url( $lostpassword_url, $redirect ) {
	$use_url = false;
	$args    = array( 'action' => 'lostpassword' );

	if ( ! empty( $redirect ) ) {
		$args['redirect_to'] = $redirect;
	}

	if ( $use_url ) {
		return esc_url( add_query_arg( $args, $lostpassword_url ) );
	}

	return esc_url( add_query_arg( $args, site_url( 'wp-login.php' ) ) );
}
add_filter( 'lostpassword_url', 'custom_lostpassword_url', 10, 2 );

/**
 * Password reset on sub site (2 of 4)
 * Replace other "unknown" password reset urls.
 *
 * @param string $url The complete network site URL including scheme and path.
 *
 * @return string
 *
 * @since 1.0.0
 */
function replace_lostpassword_urls( $url ) {
	if ( stripos( $url, 'action=lostpassword' ) !== false ) {
		return site_url( 'wp-login.php?action=lostpassword' );
	}

	if ( stripos( $url, 'action=resetpass' ) !== false ) {
		return site_url( 'wp-login.php?action=resetpass' );
	}

	return $url;
}
add_filter( 'network_site_url', 'replace_lostpassword_urls', 10, 3 );

/**
 * Password reset on sub site (3 of 4)
 * Fixes the URLs in emails that are sent.
 *
 * @param string $message Default mail message.
 *
 * @return string
 *
 * @since 1.0.0
 */
function retrieve_password_message_urls( $message ) {
	return str_replace( get_site_url( 1 ), get_site_url(), $message );
}
add_filter( 'retrieve_password_message', 'retrieve_password_message_urls' );

/**
 * Password reset on sub site (4 of 4)
 * Fixes the title in emails that are sent.
 *
 * @return string
 *
 * @since 1.0.0
 */
function custom_retrieve_password_title() {
	return sprintf( __( '[%s] Password Reset' ), wp_specialchars_decode( get_option( 'blogname' ), ENT_QUOTES ) );
}
add_filter( 'retrieve_password_title', 'custom_retrieve_password_title' );

on my multisite installation this plugin doesn't work. I try it in different ways..per functions.php as a plugin and as mu-plugin. but no luck
please help

Thank you!

Thank you very much. Works as intended on my multisite.

Still working good in 2022. Added to my child theme's functions.php file with mrjackyliang's changes.