Is there such a thing as bilateral eye cancer?

Rarely. Most eye cancers occur in one eye. Bilateral disease can be found in retinoblastoma in infancy as this is an inherited tumor commonly but not always present in both eyes. Adults get bilateral cancer in the eye in the rare instance of simultaneous metastatic cancer from another site like breast or lung.
Yes. An inherited diorder of a gene, retinoblastoma, can result in cancer on both eyes.