From a weightlifting standpoint, it may be better to think of it in terms of conditioning instead of 'cardio'.
While both cardio and weightlifting are components of physical fitness, one is aerobic, the other anaerobic. So there's always going to be a trade off. One directly detracts from the other, yet the overall improvement in fitness helps the other. The actual critical amount of either can be highly individual.
On the other hand, there are activities that are designed to increase your overall physical conditioning or 'general physical preparedness'. Examples would be sled pulling, tire flipping. medicine ball throws, farmer's walks, etc. The object here is to increase your work capacity and enable your energy system to fire more efficiently- to improve the machine.. This means you get more done in the gym in less time. The more weight you move, the stronger you get. There's no eccentric or negative portion to these exercises so it also acts as an active recovery. Westside Barbell was famous for this and is now widespread practice.
Many 'beginner' programs are also designed to do these things, both in the 5x5 and in powerlifting. If you're looking for a change of pace, a 4 or 8 week cycle can be a good choice. I've been very happy with my results doing this, as I have a limited limited amount of time I have to work out and can't always devote off days to physical activity.
The Sheiko Experiment is a short write up by an experienced lifter who's also benefited.