It's a mode of the phone that is supposed to prevent cyber attacks, more so than "normal mode" I suppose, since it's supposed to limit features in the name of security. This seems like a variant of such attack, so seems like it should protect against it
There is a documented list of things that Lockdown Mode affects [1], this is not one of the advertised ones. There are a bunch of other (undocumented) things it affects (some of which are bugs :/), but I don't believe it has any affect on notification storage.
[1] https://support.apple.com/en-us/105120