Indeed, you can have that. All you need to do is to provide proofs that you has been honorably discharged. You can use Form DD-214 from U.S. Department of Defense.
That's great. Is there any charge or fee to pay if i do this?
Not at all. I you apply and were charged a document fee, then you're entitled to a refund for the fee you paid.
I see what you mean. I'd like to ask you another question. Is it also possible for me to pick up Lyft passengers in NYC?
No, not unless you are separately authorized by the New York City Taxi & Limousine Commission
what do I need to work for a rideshare here in NYC?
You can contact one of the New York State licensed TNC companies
could I pick up Lyft customers in a taxi cab?
No, the TNC Act prohibits taxis from being used as  TNC vehicles.
what kinds of insurance would I need if I'm working for a ridesharing company?
The TNC company you work for will help you with the required insurance.
Are you interested in becoming a TNC driver or just looking for information?