1 - The dial. It may well be an original Lemania dial and it bears a resemblance to the dial style found on the one button assymetric Lemania. The aim
would be to find another reference of a military watch with the same subdial. As a note on the Lemania dials, many of the original dials were redialled by the
military - the so called MOD dial - either to make them conform to their standards or to remove the Radium and switch to Tritium (hence the circle T) and
other less nasty luminous compunds.
2 - the hands, are not typical of this type of watch, however as you rightly pointed out my watch doesn't have the "correct" chronograph hand,
more than likely replaced at some point in its life. That's why I don't hold too much store by hands being correct or not, if that were the only issue.
3 - caseback markings. Here's were things get more difficult, as BDLJ has commented. To the best of my knowledge and the research I've seen, the designation on the back of this watch is 0552/924-3316. If this is the case, then it seems that this is a unique reference given to watches that were to be used on submarines. As you can see by the MOD documents I've posted - dated 1969 and 1974. The main property of the Submarine watches were to have dials and hands with no luminous material at all, which from the pictures of your watch does not seem to be the case. I don't see a way to square this circle?
Also all British military watches were engraved and tend to be pretty neat on the whole, whereas the one you show seems atypical. In answer to your question, why not copy the correct markings, it's possible that the person who put them on did not understand them and copied them from another watch. It's not uncommon to find people copying numbers from books or other references without knowing what they actually mean.
Here is a set of Submarine Lemanias.
(Picture credit - Don Aldo - MWR Broadarrow website)
Your last question - could another military organisation have used this watch? There are a number of possible answers to this. Many different countries used Lemania one button watches, Australia, Canada, Italy and South Africa are ones that I know of, on top of that of course many other countries used NATO stock
numbers, Germany for example. So for this watch could be marked up for another countries military, with the NATO stock number (although usually there were extra marks which made them different to the UK numbers), is entirely possible. However it still would be designated a watch for use on a submarine and then it shouldn't have a luminous dial and hands.
Also to place it in context, the single button Lemania's were replaced by the Hamilton and CWC two button chronographs in the early Seventies, other countries do have examples of these. However, with the best information I know, I haven't seen any other country with the two button Lemania, which is a rare watch and seemed to have been ordered only in those two years, 75 and 76, in small quantities.
Of course we are learning new things all the time and when dealing with military watches it is not like you can always go back to the manufacturer and get information, so new things do come up. For example, the one button Breitling that Nico shows was a pretty mysterious watch only about six to eight years ago.
In terms of the movement, perhaps the Omega collectors want to chime in here. This is a movement to the two button Lemania - notice the bridge engravings.
(Picture credit - MWR Broadarrow website)
Credit - Dr No (I believe)