If the question is can Adobe Lightroom 4 run on 4GB of total system memory then yes it can, IF the question is will >4GB significantly improve the performance under 64-bit OS then yes it can.
If you're batch processing 1000~1500 images then: Fast CPU, Fast SSD, 8GB~16GB of Memory and before running the batch turn-off/disable unnecessary background applications and start-up items.
If the question is can Adobe Lightroom 4 run on 4GB of total system memory then yes it can, IF the question is will >4GB significantly improve the performance under 64-bit OS then yes it can.
If you're batch processing 1000~1500 images then: Fast CPU, Fast SSD, 8GB~16GB of Memory and before running the batch turn-off/disable unnecessary background applications and start-up items.