You should provide your code when asking this type of question. Here is an example of a header.php file. Look at the code and see how it’s done:
<!DOCTYPE html>
<html <?php language_attributes(); ?>>
<head>
<meta charset="<?php bloginfo( 'charset' ); ?>" />
<title>
<?php
global $page, $paged;
wp_title( '|', true, 'right' );
bloginfo( 'name' );
$site_description = get_bloginfo( 'description', 'display' );
if ( $site_description && ( is_home() || is_front_page() ) )
echo " | $site_description";
if ( $paged >= 2 || $page >= 2 )
echo ' | ' . sprintf( __( 'Page %s', '_s' ), max( $paged, $page ) );
?>
</title>
<?php wp_head(); ?>
</head>
<body <?php body_class(); ?>>
<div id="page" class="hfeed site">
<header id="masthead" class="site-header" role="banner">
<!-- YOUR CUSTOM LINK HERE: -->
<a href="http://lifestyle-site.com/">Switch to Lifestyle Site</a>
<hgroup>
<h1 class="site-title">
<a href="<?php echo home_url( "https://wordpress.stackexchange.com/" ); ?>" title="<?php echo esc_attr( get_bloginfo( 'name', 'display' ) ); ?>" rel="home"><?php bloginfo( 'name' ); ?></a>
</h1>
<h2 class="site-description"><?php bloginfo( 'description' ); ?></h2>
</hgroup>
<nav role="navigation" class="site-navigation main-navigation">
<?php wp_nav_menu( array( 'theme_location' => 'primary' ) ); ?>
</nav>
</header><!-- #masthead .site-header -->
<div id="main">
The part that adds the link is:
<a href="http://lifestyle-site.com/">Switch to Lifestyle Site</a>
You can also wrap it in a div tag for more css control:
<div id="custom-link">
<a href="http://lifestyle-site.com/">Switch to Lifestyle Site</a>
</div>