If an author has accepted an offer of publication and their agent is negotiating a contract with the publisher, is it common/acceptable for the author to also have the contract reviewed by a publishing lawyer before signing it?
If you want to have your publishing contract reviewed by a publishing lawyer, tell your agent. Sooner rather than later.
As most agents do, I have a boilerplate contract with all the major publishers, and a lot of the smaller ones too. This boilerplate reflects negotiations going back many years now. I know what they'll negotiate and more importantly I know what they won't.
When an author wants a publishing lawyer to review a contract, they won't know what's been negotiated previously. I'd rather have those conversations BEFORE I start negotiating on the author's behalf.
(I can still remember a writer's lawyer who wanted to change the royalty reporting periods. Not the royalties themselves, but when the reports would be issued.)
However, if you want a lawyer to advise you on the contract, a reputable agent will not stand in your way.
It's not common (at least not in my experience) but it's totally acceptable.