The one caveat to the above is that after the person enters to get their new password emailed to them, the page will redirect to the default WordPress login page.
WordPress does have "template tag" page for the lost password function in WordPress: https://codex.wordpress.org/Function.... Your developer could add the template tag to your theme to control the redirect action.
The raw PHP cannot be inserted into WordPress pages, but for those who simply want the lost password user to be redirected to the same login page, or to the home page, you can use the two examples provided on that template tag page and a plugin to allow PHP code to be placed inside your WordPress page.
The plugin PHP Everywhere allows you to insert PHP code into a page. In our testing it does not conflict with PilotPress. It provides a box in the Edit Page mode to insert PHP code into:
After you insert the code into that box, you simply place the short code [php_everywhere] on the page where you want the code inserted. To have the person submitting their lost password information to be redirected to your site's home page, use the following code in that PHP Everywhere box:
<a href="<?php echo wp_lostpassword_url( get_bloginfo('url') ); ?>" title="Lost Password">Lost Password</a>
If you want them to remain on the same page after submitting, then use this code:
<a href="<?php echo wp_lostpassword_url( get_permalink() ); ?>" title="Lost Password">Lost Password</a>