The answer is yes!
A healthy knee is a delicately balanced and quite odd system of joints. Any change in the orientation and functioning of the knee stemming from the lumbar spine (for example, a spinal segment has become stiff at the base of the spine) will alter the normal movement of one or both knees.
Now the knee may well be able to cope with this, and you may not notice any symptoms. And there may also be no symptoms in the stiffer low back.
Often though, the knee begins to grumble when you take up some new activity (e.g. running), or gain weight, or get less fit.
So bear in mind that a knee that begins to niggle for no reason may have its origin away from the knee, and the low back is a frequent (but not the only) source of this.