How can I theme or style the lost password page without a plugin?

In the file wp-login.php we can see at line 586 the following:

    /**
     * Fires before the lost password form.
     *
     * @since 1.5.1
     * @since 5.1.0 Added the `$errors` parameter.
     *
     * @param WP_Error $errors A `WP_Error` object containing any errors generated by using invalid
     *                         credentials. Note that the error object may not contain any errors.
     */
    do_action( 'lost_password', $errors );

At line 631 we have:

    /**
     * Fires inside the lostpassword form tags, before the hidden fields.
     *
     * @since 2.1.0
     */
    do_action( 'lostpassword_form' );

That means we can leave the form as is (to participate from the updates) and extend it with action hooks.

For example:

add_action( 'lostpassword_form', 'my_function_to_add_logo' ) );

Everything else depending to the layout can be done via css.

The googles came up with this page: https://code.tutsplus.com/tutorials/build-a-custom-wordpress-user-flow-part-3-password-reset--cms-23811

Basically, you create a function that does the work of the lost password page. Then you call it with this:

add_action( 'login_form_lostpassword', 'my_lost_password_page' ) );
function my_lost_password_page() {
   // code to do the lost password stuff
return;

You would place the above in your Child Theme's functions.php file.

You might be interested in the other parts of that tutorial, which discusses styling the login pages. Note that the tutorial uses a custom plugin to do all of the work, which is easiest, although you could do the same thing with code in your functions.php file. But the link might give you a starting point.

There are other links that might be useful, including the Codex: https://codex.wordpress.org/Customizing_the_Login_Form ; use that as a starting point for your efforts.