I've noticed that low light, underexposed footage produces softer images. It's like that on every camera I've used. It also depends on your contrast ratio on set, and also yes, the type of lens. It's different for every lens. Which lens is currently giving you issues?
As an example, Rokinon lenses are pretty good when it comes to resolving detail, but open any of them up all the way, especially the 24mm T1.5 and it becomes a soft mess with horrible contrast. The whites bleed all over the place, creating an even softer look. I wouldn't use the Rokinons at anything below T2 and even then, I may add a tiny bit of sharpening.
Most lenses are sharpest between 4-5.6, but some can hold contrast and detail great at 2.0. It depends on the lens.