Re. lawyers to who work here and there on a contract basis:
Yes, there are some who can do that -- only do some isolated projects for other attorneys with no long term commitments or client contacts. Like Malcat said, those attorneys are usually ones who have an excellent reputation and who are already known to the attorney offering them the piecemeal work. Also, the work product they produced is in perfectly polished and ready-for-filing condition, which is something that takes many, many years of high quality legal writing experience to accomplish.
Exactly, my point is that it's difficult to negotiate a sweet part time role unless you already have the reputation and skill to back up your value. Otherwise, why wouldn't a company just hire a normal, full time person for the job?
That said, there are also tons of companies who *can't* afford a full time person for a role and who struggle to find talented people to work part time. So if you have professional level skills, it is very possible to propose part time services to organizations that could use them.
This is similar to how almost all small businesses just use a part time book keeper. Many could also use part time marketing, part time tech support, part time financial services, etc.
You have to research your markers to understand what needs you might be able to fill with only part time services.