What you describe is paralysis of the 3rd cranial nerve which is known as the Oculomotor Nerve and in the case that you describe i.e lung cancer, one would have to consider very strongly the prospect of secondary (metastatic) spread to the brain with a grave prognosis.
Malignant disease is not the commonest cause of a 3rd nerve paralysis, but in the case that you have described it is almost certain to be.
Just one other thought..........unusual but can occur........lung cancer producing those exact symptoms with NO brain involvement.
It is called Horner´s Syndrome and caused by a lung cancer (Pancoast Tunmour) and only a Consultant Neurologist or Ophthalmologist would be able to differentiate.