lidl,
In a round about way, it could be causing your neck discomfort. The discs in the lumbar region can cause discomfort in the back, from which you can get muscle spasms, which could affect the way you are moving, which could affect your neck.
But, the discs in the lower back can press on the nerve roots directly around them, but the lumbar nerves to not travel up to the neck region. They basically supply the regions of the legs and pelvis.
Most likely the neck pain is either coming from your activities or the way you sleep on the neck. However, since you have disc problems in the lumbar region, you may also have disc problems in the cervical region. That could also be causing your neck problems.
Good luck.