When buying a new house, you usually need a lawyer to deal with all
the documents, including the mortgage.
There is regional variation in this practice. Lawyers are often need in the Northeast, but rarely in the Western U.S., although they are sometimes consulted. Many parts of a real estate transaction such as title work and real estate contract drafting from a form are considered the practice of law in the Northeast, but are considered within the competence of realtors and title company paraprofessionals in the West.
Is there any need for (or benefits from) having a lawyer involved when
simply re-financing the mortgage on an house you already own?
It can be assumed that there's no typical issues involved - current
mortgage is a normal fixed rate that is being paid on time, new
mortgage is also fixed rate, the house title has no issues, there is
no PGI insurance need for either new or old mortgage.
Probably not. The most common things that a lawyer would address are title issues such as purported liens or subordination of leases or other mortgages, problems with the settlement sheet, and understanding unusual mortgage terms (e.g. shared appreciation, a reverse mortgage, or loans with adjustable rates and balloon mortgage terms).