My client formerly changed the SSL of his website (around 3 years ago). But since then he hasn't implemented the changes in GA account and the URL shown in the account is still HTTP version.
If I update it, would I lose the previous data?
The Default URL in Google Analytics doesn't affect data collection in any way, so you can change it without any problem.
Google Analytics, by default, does not collect the host and only uses the internal path. For example, your home instead of being recorded in Analytics as
https://example.com would be just
https://example.com/landing would be
When you launch some reports that need to load the full URL, that's when Analytics uses the Default URL value to get to them. So, even if you put a wrong domain in there, data would be collected without problem. Check this link.
Website's URL: The domain name of website you're tracking, e.g.
www.example.com. This information is used by the Content reports, including In-Page Analytics.