Basically, you could use odoo studio to make a check on the other lists if a specific email address already exists. The requirement you are expressing is very special for your needs as many companies maintain multiple lists for different purposes with people being part of each list.
In order to invite each person only once, you could create a new list. You export all the lists to this very new list and delete duplicate using excel. Then you can upload the contacts in that new list that will for sure only contain each name once.
Good luck
Eva Pinter