There are lots of stories of teenagers lying about their ages to enlist (facilitated by recruiters willing to look the other way) during WWI.
Did older men ever claim they were younger than they were to get into the military? For example, men in their late 30s claiming they were in their 20s?
I can confirm at least one case in which this worked, and another in which it didn't -- though that one was a somewhat different situation.
The English author C.E. Montague (1867-1928), 47 years old as the war began, found himself bound by conscience to contribute to the war effort in whatever way he could. He had spent the war's early days writing articles and essays encouraging others to enlist, but he became convinced that he needed to participate in a more active way -- he did not want to urge others on to taking risks that he himself would not face.
Initially rejected due to his age, Montague dyed his greying hair and pretended to be over a decade younger to seek a position with the Sportsman's Battalion of the Royal Fusiliers. It was this action that caused a contemporary to declare that, while many men's hair had turned white from fear, Montague was the only man he had ever known whose hair had turned black from courage.
He arrived in France by November of 1915, but his true age was swiftly discovered and he was sent before a medical review board that kept him sidelined for several months. While he was allowed to return to active service early in 1916, this lasted for only a very short time before he was dismissed again for his age.
He remained within the service, however, receiving a series of promotions that saw him elevated to the rank of an official censor and then a member of the military intelligence corps. He eventually became a favoured tour-guide for important visitors to the front -- H.G. Wells, George Bernard Shaw, and even the Prime Minister David Lloyd George. He had become somewhat disillusioned with the war effort on the whole, and seemed to delight in getting these celebrities a bit closer to the action than they had intended.
After the war's conclusion he set about writing a book that would upend the conflict's literary landscape in Britain -- Disenchantment (1922), which set the tone for many of the aggrieved and critical memoirs that would follow during the "war books boom" of 1927-1933 that saw the publication of major works by the likes of Hemingway, Sassoon, Graves, Remarque, Brittain and others.
Another example might be found in the form of Sir Arthur Conan Doyle (1859-1930), who was considerably older during his numerous attempts to join the British Army. He also made no effort to hide his age, however, and -- as an international celebrity -- could not very easily have done so. In his defense, he declared:
"I think I may say that my name is well known to the younger men of this country and that if I were to take a commission at my age it would set an example which might be of help... I am fifty-five but I am very strong and hardy, and can make my voice audible at great distances, which is useful at drill."
As you know that Sir Arthur wasn't killed in action, you might easily anticipate the result.
He was rejected time and again, in spite of his enthusiasm, and he eventually settled for creating a private home defense battalion to protect against the possibility of German invasion. This in turn became a sort of nightmare for the War Office, who considered Doyle to be an extreme nuisance and his battalion a joke, but as the war dragged on they began to see the potential wisdom of the idea. They decided to formalize the creation of a home defense corps, and they offered him command of the Crowborough Company of the Sixth Royal Sussex Volunteer Regiment. Doyle, wishing to set a good example, demanded that he instead be signed on as a private.
I had hoped to say more about Ford Madox Hueffer (later Ford Madox Ford; 1873-1939), who abandoned his life as an author and propagandist to enlist; he was 41 when he arrived on the Western Front in 1915. I don't currently have access to any details about whether or not this was difficult for him, however, and can say only that he performed his duties admirably and went on to produce some of the most excellent books about the war to emerge in the succeeding decade -- the Parade's End tetralogy.
Your question rightly highlights that this is a remarkably understudied aspect of voluntarism during the war, especially when compared to the huge amount of work that has been done on those who were underage. I wish I had more to tell you beyond the above anecdotes, and I'll be sure to return to add more details as I uncover them.