Moving from New Jersey to Georgia. Is it advisable to have a lawyer besides the closing lawyer assigned by the realtor?

there is a lawyer already working with the realtor?  And that attorney is for both the buyer and the seller?  I'm not sure from your question - but many states do not require a lawyer to handle the closing.  as long as your realtor, or you, or someone on your behalf is advocating for the conditions of purchase or sale that you want, then you will be fine and will not need another attorney.