Option C: “I” provides the sentence meaning. The sentence then means that, “Both of us will go to the theatre tonight.” Hence this is the correct option.
Option A: “eyrie” refers to the nest of a carnivorous bird, built at a high altitude. This is irrelevant in the given case. Hence, this option is incorrect.
Option B: “eye” does not provide the sentence with any meaning. This is irrelevant in the given case. Hence, this option is incorrect.
Option D: “I’ll” is the shortened form of “I will”. If used the sentence would become, “He and I will will be going to the theatre tonight.” Which is incorrect. Hence this option is incorrect.