Mitochondrial ornithine-citrulline antiporter (Probable) (PubMed:12807890, PubMed:22262851). Catalyzes the exchange between cytosolic ornithine and mitochondrial citrulline plus an H(+), the proton compensates the positive charge of ornithine thus leading to an electroneutral transport. Plays a crucial role in the urea cycle, by connecting the cytosolic and the intramitochondrial reactions of the urea cycle (Probable) (PubMed:12807890, PubMed:22262851). Lysine and arginine are also transported by the antiport mechanism (Probable) (PubMed:12807890). In addition, catalyzes an electroneutral exchange of ornithine or lysine for H(+), a reaction driven by the pH gradient across the inner membrane (By similarity).