It would depend on how you set up your security. If you set up your Everyone on the internet user Security role that they can only 'Add' records then each of their entries would result in a new submission. You are able to modify their role to be able to EDIT any record as well, so security wise you CAN have them modify existing entries but that comes with quite a bit of risk so beware.
The only change you have to make is to change the Modify access to whatever role is assigned to the EOTI role. However - for them to edit the record they would need a link or some kind of reference in order to actually get to an existing record. So for example if your external users are currently entering new leads from a link on a website - that link is likely to add a new record. If you needed them to be able to edit/update their own lead submission - you would need some way, such as emailing them, to provide them a direct link back to the record with the Record ID# in tact so they can navigate back and make edits. The risk here though is that anyone with that link could then access it. You can't control if Person A sends the link to Person B and then stop Person B from making changes from it. There are some 'fake' security measures - such as making a email workflow where you send them a code they have to enter before they can make edits - can of like a fake 2-Factor authentication but you'll have to devise what makes the most sense if you wanted to fake your own security controls.
