If you are using DNN 4.3.x or 3.3.x then yes it is possible to prompt a user for any additional info you request when they first login.
You set this in the profile properties page, and its outlined in this tutorial:
How to Manage Profile Properties in User accounts (Creating a custom registration page)Setting form fields to required in the profile properties section will ask a user to fill out any additional details when they log in. - All of the step are outlined in the videos above.
Things maybe a little more complicated for you however as your users are in a separate database, so you may not be able to use the manage profile properties facilities that come built into DNN.
If this is the case, you are going to need to write some code to check the user when they first login to see if they have an email address, if they do not then direct them to a form to request the email address.
If you need help with coding then I would pop across to the main DNN forum.
Thanks,