The government isn't immune to suits regarding infringement of freedoms, failure to disclose information that it's obligated to disclose, etc. Think of how many ACLU lawsuits there have been, for example.
But in many cases the ACLU fights those cases on defense. If the government charges me with "unlawful speech," for example, there's nothing stopping me from retaining ACLU lawyers as part of my legal team. Or if I'm convicted, the ACLU can step in and offer to help with my appeal, in the interest of bringing the judgment to a court with sufficient standing to create precedent. But neither of those things is exactly the same as "suing the government."
In the case where information is not disclosed, I think far more often the procedure is not to try to sue, but first to demand that the agency that possesses that information disclose it; then demand that whichever agency has regulatory authority over the first agency step in and do something about it; and then make sure the New York Times knows all about it; and then call a couple Senators and Representatives about it; etc.
And then in some cases the government just agrees to be sued because a judgment in the government's favor would establish precedent and get the ACLU out of its face. And sometimes the government loses those.