It's complicated, but under certain circumstances you can sue agencies for not doing something. It depends on the specific laws governing the specific agency and how you've been harmed by the inaction. Broadly speaking, the Administrative Procedures Act required agencies to have procedurally fair processes. If you're concretely harmed by an agency's inaction and you can show they didn't follow the correct processes, you can sometimes win.
The general rule of US and English common law is that the sovereign is immune from liability. The reason you can sue the U.S. Government is because Congress passed laws such as the Tucker Act, the Federal Tort Claims Act, the Administrative Procedures Act, and Section 1983 of the Civil Rights Act allowing plaintiffs to do so.
Judicial review doesn't generally let you sue the Government to obtain redress for injuries; it is for enforcing the people's Constitutional rights where the Government is stepping out of bounds. It doesn't let you, say, sue the FTC to get them to do their job.