In King Lear, Edmund, resentful of his inferior status to his older brother, betrays his family and frames his brother as a traitor. This strikes me as being quite a bit like what Edmund does in The Lion, the Witch, and the Wardrobe. Is there any evidence of an inspiration, or is the resemblance purely coincidental?
As far as I’ve been able to find, Lewis never spoke explicitly about a connection, but as Rand al'Thor noted, others have made the same connection. David L. Johns offers a full chapter in Quakering Theology making the case that the two Edmunds are connected which is fairly compelling. But without any explicit statement from Lewis, we can never say for certain, even if it is likely that Lewis did make the deliberate choice to name his Edmund after Shakespeare’s.