Bilski doesn't apply here, as the In Re Bilski ruling only applies to Process claims. The claims in question are directed to a system.

Actually, a lawsuit is "valid" (whatever that means) when it is filed with the court. The next thing that happens is that notice that the lawsuit has been filed and a copy of the suit are served on the defendants. This can happen many different ways and varies depending on what jurisdiction you are in. In Ohio, for example, Certified U.S. Mail is the preferred means of service of summons, with other means (such as personal service and service by publication) available if Certified Mail fails. Service of summons is not a subpoena. (A subpoena is an instrument that compells the receiver to appear in court at a specified date and time - service of summons does not do that directly).