<The doubtful Medley game first appeared in the London <Era> of January 2, 1859, as a Medley-M game. Very evidently the "M" stood for Mongredien and not for Morphy, for Mongredien was mentioned in the notes to the game, and it never appeared on any list of Morphy games at the time.> (Kindle ed., ULPress, 2010)

Here's the relevant section of the January 2nd column (p.5):

<We have lately, through the kindness of Mr. Medley, the Honorary Secretary of this club, had several fine games placed at our disposal illustrative of the attack in the Evans Gambit, which we shall from time to time lay before our readers. The members of the London Club now practise their favourite game with much energy and spirit, and Herr Lowenthal has accepted an invitation to be present each Friday evening, and enjoy a contest with Mr. Mongredien, one of its strongest players, during the winter season.>

Then comes the game. Whilst I accept that Lawson is likely correct to equate <Mr. M> with Mongredien, it's not quite as explicit as he proposes. Mongredien's name features in the (above) introduction to the game but not the <notes to the game>, as we now understand the term.

Not Mongredien, but rather Mr. Maude. The <Era> of 1859.05.22 gives a game with the same series of moves up to 18.Nbd4. The note to 14.Qa4 in that game states "In our notes on a game previously published, played by these gentlemen, we had occasion to remark on the novelty of this move, which is one of Mr. Medley's invention."; turning back to the game published on 1859.01.02 Lowenthal did indeed remark upon this move with "At this stage of the Evans Gambit opening it is of great importance to bring the Q R into speedy action, and we beg the attention of the student, and our readers generally, to this clever device of Mr. Medley's for effect the desired object."