Most people tend to be discussing either some mediocre weightlifting that doesn't send you into a high-stage of fatigure, or as many people mentioned, have placed at least 6 hours between their time in the gym, and their time training the chosen MA. These are cases that I also tried to specify above.
If you have significant amounts of time in a chopped schedule to do weightlifting in the morning or mid-afternoon, then do BJJ at night, that's fine. You're at least giving yourself some time to cool down, get some fresh blood going.. Hell, even eat a meal and take a nap if you want to.
But as I said above. If you're a gymrat that can move metal by the metric fuckton, you're going to be far too exhausted after a weight-lifting session to have a safe training class. IF you don't hit the weights hard, and just do 2 medium sets on a muscle-group before moving to another section, this is a different type of weight-lifting. Many of us consider this more as a suitable "Warm Up" before training. There's a huge difference in intensity factors to be taken into play.
When I lift weights, I lift hard, and usually have a hard time holding a cup/glass/bottle of water steady to drink from for up to an hour afterwards. THAT kind of training could be heavily detrimental if a training regiment in the martial arts were to follow immediately, and could lead to a serious injury. If I was lifting only 50-70% intensity for 15-25 minutes without exhausting any major muscle-groups, then I would consider that a before-class warm-up.