Is a lawyer working on a case allowed to short the stock of his client?

Why not?

(Hint: it creates a perverse incentive to see your side lose the legal argument for your own personal gain.)

And in this case, it's the actual secretary doing it. Who has significant influence on the outcome of the case (largely in the negative - nothing he can do can make the government more likely to win it, but stuff he did has the capacity to make the government more likely to lose it.)