When you click on the Edit tab of a profile, the field for e-mail address is at the very end of the 'Edit Data' section. There is a link with the field that you can use to cause an invitation to be sent. If you're not able to locate it for some reason, please post again and indicate a sample profile that you're having a problem with, so someone can take a look.
Note that the e-mail field would not be present for a deceased person. If there is an entry for date of death, you wouldn't expect to find that field.