There is not a native tag in EE for outputting the "forgot password" form into an EE template.
A "creative" option would be to strip down the native member template to bare minimum HTML and load the form into your template using jQuery.
JS would look like this:
<script>
$('#result').load('/member/forgot_password');
</script>
HTML would look like this:
<div id=""></div>
The tag to access the native EE forgot password template is {path='member/forgot_password'} OR replace "member" with the member profile trigger word you have set in your CP. Or just use "/member/forgot_password".
You can submit the form via ajax as well so you don't have to show the default system message, or submit the form and show the system message.