Legal Question in Employment Law in California

Presumably, you have not been served with the lawsuit, which means you are not subject to the jurisdiction of the court and therefore not yet a party to the suit. Therefore, there is no harm done and no basis for a suit.

If the employer or its attorney has accepted service of the suit on your behalf and is representing you without your knowledge, there are some ethical issues that need to be addressed. You should be discussing this with the employer and asking whether they are representing you in the case. You should know you have the right to your own representation, if you believe there is a conflict of interest and in some cases, the employer may have to pay your legal fees.

Mr. Kirschbaum's answer is correct, but doesn't answer your question directly. The answer is "no." You cannot sue your employer for not notifying you of being named in a lawsuit. If you have not been served with the summons and complaint, you are not actually a party to the suit yet. If you have been served, you already know about it and your employer doesn't have to tell you what you already know.