Set content type to HTML for lost password email only

I suspect you implemented the hook something like this:

function wp_set_html_mail_content_type() {
    return 'text/html';
}
add_filter( 'wp_mail_content_type', 'wp_set_html_mail_content_type' );

More info: https://codex.wordpress.org/Plugin_API/Filter_Reference/wp_mail_content_type

Did you need to reset the content type at a later point?

** UPDATE: try intercept it with a global variable:

function xxx_wp_email_content_type() {
    if($GLOBALS["use_html_content_type"]){
        return 'text/html';
    }else{
        return 'text/plain';
    }
}
add_filter( 'wp_mail_content_type', 'xxx_wp_email_content_type' );

function xxx_wp_retrieve_password_message( $content, $key ) {
    ob_start();

    $GLOBALS["use_html_content_type"] = TRUE;

    $email_subject = xxx_wp_retrieve_password_title();

    include( 'templates/email_header.php' );
    include( 'templates/lost_password_email.php' );
    include( 'templates/email_footer.php' );

    $message = ob_get_contents();
    ob_end_clean();

    return $message;
}
add_filter( 'retrieve_password_message', 'xxx_wp_retrieve_password_message', 10, 2 );