You would lose an effort to get a court to compel the DOJ to pursue the perjury case. Where a public official has the authority to exercise discretion in a matter then it is up to that official how he or she chooses to act. It is not the role of the courts to tell executive agency officials how to do their jobs. A lawsuit to compel a public official to carry out some act of his office is known as a writ of mandamus. The rule in the federal system is that a court may issue a writ of mandamus to compel a public official to carry out a purely ministerial act (i.e. one that requires no discretion on the part of the public official) but a court cannot compel a public official to do an act that falls under his/her discretion. The rule is an old one. As far back as the case of Marbury v. Madison (which is famous for another principle not relevant here) the Supreme Court made this very distinction:
The secretary of state acts, as before observed, in two capacities. As the agent of the President, he is not liable to a mandamus; but as a recorder of the laws of the United States; as keeper of the great seal, as recorder of deeds of land, of letters patent, and of commissions, &c. he is a ministerial officer of the people of the United States. As such he has duties assigned him by law, in the execution of which he is independent of all control, but that of the laws. It is true he is a high officer, but he is not above law. It is not consistent with the policy of our political institutions, or the manners of the citizens of the United States, that any ministerial officer having public duties to perform, should be above the compulsion of law in the exercise of those duties. As a ministerial officer he is compellable to do his duty, and if he refuses, is liable to indictmen
Marbury v. Madison, 5 U.S. 137, 149–50, 2 L. Ed. 60 (1803). And again, a few decades later, the Supreme Court stated the following:
The Court could not entertain an appeal from the decision of one of the Secretaries, nor revise his judgment in any case where the law authorized him to exercise discretion, or judgment. Nor can it by mandamus, act directly upon the officer, and guide and control his judgment or discretion in the matters committed to his care, in the ordinary discharge of his official duties.
Decatur v. Paulding, 39 U.S. 497, 515, 10 L. Ed. 559 (1840). It is not the role of the courts to tell the executive branch how to carry out its discretionary functions. The courts are not to dictate how the executive branch functions. The Supreme Court in Decatur makes this very point:
The interference of the Courts with the performance of the ordinary duties of the executive departments of the government, would be productive of nothing but mischief; and we are quite satisfied that such a power was never intended to be given to them. Upon the very subject before us, the interposition of the Courts might throw the pension fund, and the whole subject of pensions, into the greatest confusion and disorder.
Id. And while it is an old rule, it is still very much the current law. In a case involving a similar situation in which a person who sought mandamus to compel the FBI to undertake certain investigations and take certain enforcement action, the a federal district court stated:
Mandamus may be used to compel a specific duty or act, but may not be used where the order would interfere with the exercise of a discretionary act....Golub's claim is focused on what the FBI should be doing and how it should be done. The claim does not rest on any duty owed by the FBI to him. The kind of agency action that Golub challenges here, the failure to investigate or take enforcement action against certain alleged illegal activities, is a decision generally committed to an agency's absolute discretion. See Heckler v. Chaney, 470 U.S. 821, 831, 105 S.Ct. 1649, 84 L.Ed.2d 714 (1985) (citations omitted). Because it is discretionary, an agency decision not to investigate or enforce is not suitable for judicial review. Id.
Golub v. F.B.I., No. 1:09-CV-01064-TWP, 2010 WL 3523009, at *1–2 (S.D. Ind. Aug. 31, 2010).
Nor may you sue the federal government for money damages for this. The federal government is immune from suit for money damages under the doctrine of sovereign immunity except to the extent Congress has waived sovereign immunity and consented to be sued. The Congress enacted the Federal Tort Claims Act as a waiver of immunity allowing citizens to sue for injuries from most negligent acts of federal officials. The problem is that this is not a negligence matter. The government does not owe you or any other specific individual a duty to prosecute a crime. Rather, the government prosecutes crimes for the benefit of society as a whole. Without a specific duty owed to you there is no good negligence action. There is also a waiver of sovereign immunity for instances where the government has violated your civil rights, but declining to prosecute a crime is no violation of any of your civil rights. You do not have a right to compel the government to prosecute any matter.