I think it's a broader question for everyone in forum but here are my inputs
1. Do you export the data before it's purged? If so, do you use Data Feeds to accomplish this or another method?
Yes, it's always a good practice to export the data using data feed (which is every hit you send to adobe data collection server) or data warehouse (copy of Analytics data on which you can apply filters (segment based) and breakdown etc)
2. For storing the data, do you put it in a data lake never to be referenced? Or do you restructure it somewhere?
I have seen customers using their data lake system to store it and they can leverage the same to restructure or create their own reporting system
3. Is this an in-house process or do you work with a third party to make the data useful again?
it varies from company to company there are companies who have those managed from third parties but there are some who has in house capabilities to manage it at their own.