C.S. Lewis used no pen name for his 1940 book The Problem of Pain.
The Problem of Pain was published under Lewis’s own name in 1940. It examines why suffering exists if God is omnipotent and good, and it discusses subjects including divine goodness, human freedom, punishment, and hell. The book was one of Lewis’s earliest major works of Christian apologetics.
Lewis did use pen names for some other publications, which makes this a useful distinction. His early poetry appeared under the name Clive Hamilton, while A Grief Observed was first published in 1961 under the pseudonym N.W. Clerk. Those separate cases do not apply to The Problem of Pain.
The book is also sometimes confused with Lewis’s later treatment of personal grief. The Problem of Pain presents a theological argument, whereas A Grief Observed records the raw emotional experience following the death of his wife, Joy Davidman.