Lewis discusses why we should take the OT seriously with the Christian second meanings, etc. He give 2 reasons.
The first is basically an argument based on secular literature and how second meanings could be imparted without knowledge. In the midst of this he writes, "I cannot be he only reader who has wondered by God, having given him [St. Paul] so many gifts, withheld from him (what would to us seem so necessary for the first Christian theologian) that of lucidity and orderly exposition.”
The second reason is more compelling for Lewis (and for me). Jesus himself uses the OT to refer to himself.