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Fix to the key search in both lists.
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Decrypt the ciphertext with every possible key and store the result: $2^{56}$ decryptions. Now encrypt the (known) plaintext of the ciphertext with every possible key: $2^{56}$ encryptions. Now you have to check every entry, which is in both lists and try it with another plaintext-ciphertext pair. If you can successfully decrypt that, you are very likely to have found the correct key. All in all $2^{56} + 2^{56} = 2^{57}$ operations, not $2^{112}$. Just the normal Meet-in-the-middle attack.

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