First American Financial Corp., one of the biggest title insurers in the U.S., was sued by a client who claims the company’s lax security measures put him at risk of identity theft, along with millions of others whose personal information could be easily accessed through its website.

Pennsylvania resident David Gritz, who bought and flipped multiple houses, contends that First American Financial and First American Title “allowed anyone to access sensitive files of millions of customers,’’ by using document identification numbers that were sequential.

The lawsuit filed Monday in California follows the revelation Friday in an article by Brian Krebs,...