L-Ornithine is a nonprotein amino acid (not used to create proteins) that is an intermediate of the urea cycle, and provision of ornithine to a cell is actually the rate limiting step of the cycle. Ornithine binds with a molecule known as carbamoyl phosphate which requires ammonia to be produced and then is converted into L-Citrulline giving off urea as a byproduct. Due to this, the conversion is one that reduces ammonia concentrations in the blood and concomitantly increases urea.
L-Ornithine is thought to be important for conditions that are characterized by an excess level of ammonia, and this is mainly focused on either hepatic encephalopathy (clinical liver condition) or prolonged cardiovascular exercise. A reduction in serum ammonia has been repeatedly found in persons with hepatic encephalopathy (most studies use infusions, although it appears to apply to high dose oral supplements as well) while there are only two studies assessing exercise; the one that was better suited to assess the influence of ammonia (using prolonged exercise rather than acute exercise) did find an anti-fatigue effect.
Furthermore, reductions in self-reported fatigue have been noted in persons with hepatic encephalopathy and in persons subject to a hangover (the process of getting drunk off of alcohol will increase serum ammonia) when ornithine is taken before drinking, but only in persons sensitive to alcohol perhaps.
There is currently one study using ornithine paired with arginine that noted improvements in lean mass and power output in weightlifters, but this is an old study that has not been replicated and its practical relevance is uncertain.
Finally, the increases in growth hormone seen with ornithine are similar to those seen with arginine. Technically they exist, but as they are very short lived and the body seems to compensate the overall increaes in whole-day growth hormone are not significant. Since the main properties of growth hormone being concerned with (increased lean mass gain and fat loss) are more related to day-long exposure rather than short-bursts, it is unlikely that ornithine has a role here.
In the end, ornithine looks somewhat promising for reducing ammonia concentrations in the blood and thus enhancing performance of prolonged exercise (45 minutes or more) which is in part due to it being elevated in the blood for a few hours after ingestion despite exercise.