Named after the famous writer C.S. Lewis (1898-1963) who was born in East Belfast. Best known for his series The Chronicles of Narnia, Clive Staples Lewis was also a literary scholar and lay theologian.
Note that Lewis Court is located off Euston Street and is not in the vicinity of the group of streets near Connswater named after C.S. Lewis.
See Martin Magill's blog on street names connected with Lewis: https://www.belfaststreetnames.com/streets-of-cs-lewis/