There is no way to recover messages that have been deleted on your phone.
If these messages were important from a legal point of view you may want to contact the Verizon Wireless Legal Department.
If I need deleted texts/picture messages, on what grounds do I have to have to get a subpoena?
You don't say what you need them for, so how can we possibly tell you what the grounds would be?
Best to speak to your lawyer. If they aren't important enough to speak with a lawyer, chances are you don't have grounds for a subpoena.