A non-lawyer can bring torts committed against them in their own name as pro se parties in their own name. They cannot sue for torts committed against others including entities in which they are officers, or persons for whom they are guardians, nor can they represent someone else in their efforts to do so.
A handbook written for California judges does not anywhere suggest a greater limitation than that. Neither does a guide for pro se parties in federal courts in California (see also here). Labor law and civil rights claims are routinely filed pro se in California's federal courts. California's state courts have standard court forms for pro se parties to use in state court to sue for torts like personal injury and fraud.
The comment that: "[L]ay people can't prosecute [torts] in California", appears to be not literally true. Either the implied meaning was that they cannot prosecute torts committed against someone other than themselves, or the comment was mistaken. It is also possible that the person making the comment meant that it was not as a practical matter possible to be successful in doing so because it is so difficult.
There may be a limited exception for law students in a legal clinic working under the supervision of a law school professor.