We have a list called employee details, which has client name as one of the columns which is of the type lookup (from another list name columns value). So when the users create a new item in the employee details list, I want a workflow to trigger and an email (with details) to be sent to the employee whose name is selected from the drop down box. Since client name is not a people picker column, how is it possible with OOB? If not any custom solutions?
AFAIK, the send email activity will try to resolve the string into a principal and get its email address. Please try giving valid user names and check it.
There is also a OTB condition available in SharePoint Designer which checks if provided value is a valid sharepoint user. You may want wrap sending email under that condition.
UPDATE: I tested that if you specify a string (which let's say is coming from a dropdown or a textbox), send email activity sends email as long as;
the string represents display name of user (like Patel, Ashish) or
Active directory account name (like mydomain\ashish.patel) AND
Email is associated with the user profile.
Is the email address defined in your employee list at all?
If it is, since you've used lookup columns to define the user, you know the corresponding list item id and can lookup any corresponding field in the list item. If one of those fields is the user's email address, you can store that in a variable and use that as the To: address in your workflow email.