Legal Question in Civil Litigation in California

No. A complaint (document initiating a lawsuit) must be served personally on the defendant.

With a summons.

That depends on who the "someone" is, why she's being notified, and where the notice came from.

If she's a defendant and the notice is supposed to bring her into the case then the answer is no, unless she consented to accept that type of notice ahead of time.

But if the papers were properly served on her lawyer or other authorized agent and then she found out about it via email, there wouldn't be a problem. She'd have been properly served even without the email.

There are many possible scenarios, even if the "someone" was the defendant and the sender was the plaintiff. There are many more if other people sent and/or received the email instead.

One that leaps to mind is a class-action lawsuit, where the lawyers representing the class have to notify each of its members at various stages. That might often be allowed via email.

Since you haven't given us a lot of information, I can't be more specific.

Email is not a valid form of service of a summons and complaint.