Brief Answer:
It is probably ptosis and requires evaluation.

Detailed Answer:
Hello
Welcome to Health care magic

It seems from the history that you are having problem of left eye getting smaller and wants to close involuntarily. I guess this probably means drooping of the upper eyelid resulting in ptosis and your physician wants to rule out sympathetic parlaysis secondary to cancer in thorax.

This can be a possibility and this can be ruled out by CT of thorax.

If this is absent other cause like third cranial nerve problems, diseases affecting the muscles of the eyelid or aponeurosis of the eye lid needs to be considered.

If possible do send a photo of the affected eye so that I can confirm the diagnosis and suggest you proper investigations.

Hence I would like to say this is a problem and requires evaluation to find out the underlying cause and treatment accordingly.

Hope the information is helpful to you.

Thank you
with regards

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