Not if you have not previously backed them up with some sort of SMS backup tool. If you are unsure if you have done so, you most likely have not.
Are you talking text messages or voice mail messages? if text messages, nothing you can do with lost messages, but there is a setting in Settings/Messages that indicates how long to keep messages: Forever, 30 days, or 1 year.
You can check your Verizon Cloud:
Going to My Verizon>My Device>Back up my contacts gets you there in 1 click.
Integrated messaging saves them automatically for 90 days.