Core Trac: https://core.trac.wordpress.org/ticket/37522

Problem
WordPress provides wp_login_form() in wp-includes/general-template.php which allows developers to embed the login form anywhere on a site via themes, plugins, or shortcodes. However, no equivalent function exists for the lost password form. Developers who need to embed a lost password form outside of wp-login.php are forced to either copy raw HTML from core into their own code, redirect users to wp-login.php?action=lostpassword (breaking custom branding), or rely on third-party plugins — all of which are undesirable alternatives.

Root Cause
The lost password form has always been hardcoded as inline HTML directly inside the case 'lostpassword' block of wp-login.php with no reusable function wrapping it. While wp_login_form() was introduced as a proper reusable function following WordPress coding standards, the lost password form was never given the same treatment, leaving a gap in the API surface.

Solution
Introduces wp_lostpassword_form() in src/wp-includes/general-template.php, following the exact same pattern and conventions as wp_login_form():

src/wp-includes/general-template.php — New function wp_lostpassword_form():

Accepts an $args array with configurable options: echo, redirect, form_id, id_username, id_submit, label_username, label_submit
Fires the existing lostpassword_form action hook inside the form (already documented in core since 2.1.0)
Adds three new filters for extensibility: lostpassword_form_defaults, lostpassword_form_top, and lostpassword_form_bottom — mirroring the login_form_defaults, login_form_top, and login_form_bottom filters on wp_login_form()
Returns or echoes HTML based on the echo argument
Reads $_POST['user_login'] safely to repopulate the username field on failed submissions
src/wp-login.php — Updated case 'lostpassword':

Replaces the inline hardcoded form HTML with a call to wp_lostpassword_form(), passing $redirect_to as the redirect argument
Ensures wp-login.php and any custom embed use identical markup going forward
Developers can now embed the lost password form anywhere:

// Echo directly
wp_lostpassword_form();

// Return as string (e.g. for a shortcode)
add_shortcode( 'lost_password', function() {
return wp_lostpassword_form( array( 'echo' => false ) );
} );

// With custom redirect
wp_lostpassword_form( array(
'redirect' => home_url( '/account/' ),
) );