This isn't obvious to me.
I would guess that the inventor has the burden of creating the specifications and then the attorney would formalize it into legal language.
But when it comes to the claims, it's not obvious where is the division of labor between the inventor and the attorney.
This is my opinion as an inventor. The inventor's burden is to communicate the invention to the lawyer. This includes any known background, relevant patents and other prior art. You should describe how the invention works, possible embodiments including those that are not preferred. You should provide drawings and data supporting the description of the invention. The inventor should think about how one might design around the invention and relate those thoughts to the lawyer. If any other people worked on the invention then the attorney needs to know who they are and what they contributed.
The lawyer will draft both the specification and claims. The lawyer should explain the spec and claims and be willing to adjust them if you don't think they capture the novel aspects adequately. You can try drafting something like a specification as part of your communication to the lawyer, but don't be surprised if virtually none of it ends up in the patent application.
Specifically about claims - the drafting of claims is a very particular skill. The rules of interpretation of claim language are arcane and a moving target. Definitely not for the inventor to work on.
But the inventor/business person is key in determining the aspects of the invention/potential product that are valuable to the customers/users. You want to claim aspects that provide significant value and differentiation.
If someone makes a competing product that skirts the edges of your claims will the customer see a significant difference in function or price? Patents are a business tool.
