I think something like this should work:
$customer = Mage::getModel('customer/customer')
->setWebsiteId(Mage::app()->getStore()->getWebsiteId())
->loadByEmail($yourCustomerEmail);
if ($customer->getId()) {
try {
$newResetPasswordLinkToken = Mage::helper('customer')->generateResetPasswordLinkToken();
$customer->changeResetPasswordLinkToken($newResetPasswordLinkToken);
$customer->sendPasswordResetConfirmationEmail();
} catch (Exception $exception) {
Mage::log($exception);
}
}
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