The answer is yes!
A 'normal' 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 joint 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 be no symptoms from the stiffer low back either.
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 common source of this.