What's wrong with selecting a lawyer who already has such a clearance?
According to an article I read elsewhere, the attorney already has a TS clearance. But, that doesn't mean she is "read in" to the program in question.
Although the same federal agency does all clearance investigations, every sponsoring federal agency has their own set of requirements for a given clearance level. And especially at the TS level, individual programs can have additional requirements.
If someone already meets the requirements, it's just a matter of making the request. But, the program sponsor has to make or approve the request. And, it looks like the State Dept. is being passive aggressive to deny these whistleblowers access to independent counsel.
I emphasized independent for a reason: the only lawyers with the necessary clearance are probably already working for the State Dept. And frankly, I wouldn't want them representing me.