Well, one needs to only look at what Andrew's aunts name is...Mrs. LeFay. Lewis drew the name from Morgan LeFay in the Arthurian Legends. While it may be simply implied that she is Morgan from the legends. It's nto to say she couldn't be both the Morgan from Arthru's stories and an Atlantian. If in That Hideous Strength Merlin is from Atlantis then she could be too.
As for how Morgan could came upon it, if she were Atlantian I'd like to submit Clarke's Third Law: " The Technology of any suffiecently advanced culture woudl appear as indistingushable from magic to the unadvanced mind." Basically according to the legends ( which both Lewis and Tolkien adhered to in their own legnedarium) Atlantis was the most advanced civilization ever. This would mean by some means they could develop the means of making the extra-demensional journey to the wood between the world.
It could also help retcon Jadis's origin too. Remember how in TL,TW,TW, ( novel.) Mr. Beaver said that the witch was descended from Lilith, Adam's first wife? Well, That is how she could both be from Charn and descended from Lillith. Lillith's clan makes the journey to Atlantis, dsicovers the means to get to Charn, and takes it over by there sheer force of will. Then over time the gradually grow worse and worse untill Jadis desrtoyed it with the Deplorable Word.
Meanwhile in our world, Atlantis sinks, Morgain and Merlin head to Briton and the rest they say is history.
My theory at least.