I can't remember when date_of_last_access was available in the participant administration, at least it wasn't in EFS-Survey 8.2.
If it isn't available by default, I don't think that there's a way to change that.
Question is, how much data are we talking about? If it isn't much, you could save it in user defined participant variables.
Which data is gathered first, the Unipark one or the external one?
If Unipark is gathered first, you could add the LFDN of the participant to the external data, if the external data is gathered first, maybe there's some sort of identifier you could save in the aforementioned variables.
If you are using a personalized survey, you could also request the rights for the combined adress- and results-data. This way, the export would show you the participant's name together with the gathered results. As this is connected to privacy data security issues, please contact firstname.lastname@example.org
to get access to this feature.