Final answer:
The abducens nerve, also known as the sixth cranial nerve, is responsible for the innervation of the lateral rectus muscle of the eye, facilitating eye abduction.
Step-by-step explanation:
The cranial nerve that supplies innervation to the lateral rectus muscle of the eye is the abducens nerve. This nerve is specifically responsible for abducting the eye, which it achieves through the contraction of the lateral rectus muscle. It is also known as the sixth cranial nerve and plays a crucial role in coordinating eye movements by connecting to neurons in the abducens nucleus of the superior medulla.