Vincent's NT Word Studies
12. Without law (anomwv). Both law in the abstract and the Mosaic law. The principle laid down is general, though apparently viewed with special reference to the law of Moses.In the law (en nomw). Rev., under law, i.e., within the sphere of. No decision as to the reference to the law of Moses or otherwise can be based on the presence or absence of the article. Nomov law, is used both with and without the article for the Mosaic law. Cremer correctly says that "the article is usually wanting when the stress is laid, not upon the historical impress and outward form of the law, but upon the conception itself;" or, as Bishop Lightfoot, "law considered as a principle, exemplified no doubt chiefly and signally in the Mosaic law, but very much wider than this in its application."
Shall be judged (kriqhsontai). The antithesis shall perish suggests a condemnatory judgment. There is no doubt that the simple krinw is used in the New Testament in the sense of condemning. See John iii. 18; 2 Thessalonians ii. 12; Heb. xiii. 4. The change from perish to judge is suggested by by the law. "The Jews alone will be, strictly speaking, subjected to a detailed inquiry such as arises from applying the particular articles of a code" (Godet). Both classes of men shall be condemned; in both the result will be perishing, but the judgment by the law is confined to those who have the law.
Robertson's NT Word Studies
2:12 {Have sinned} (hemarton). Constative aorist active indicative, "sinned," a timeless aorist. {Without law} (anom"s). Old adverb "contrary to law,"unjustly," but here in ignorance of the Mosaic law (or of any law). Nowhere else in N.T. {Shall also perish without law} (anomws kai apolountai). Future middle indicative of apollumi, to destroy. this is a very important statement. The heathen who Sin are lost, because they do not keep the law which they have, not because they do not have the Mosaic law or Christianity. {Under law} (en nom"i). In the sphere of the Mosaic law. {By the law} (dia nomou). The Jew has to stand or fall by the Mosaic law.