The signature looks somewhat thick and sloppy. The outer track does not have 1/5 second markings, which is unusual. The font of the numerals in the outer track does not look right. Dial looks in decent condition and yet all of the luminous material is gone. The minute hand does not reach the outer track. Given that the watch is from the late 1930s, one would expect to find a second hand with a circular counter poise rather than this style, which is more typical of the 1940s. Have you seen a hooked 7 without any curves? I have to look more but this seems atypical too. Below is a larger 3T with a 12.68Z, rather than a 10.68Z, for comparison.
The dial certainly looks like it has been cleaned. The flat look makes it appear like the lacquer has been removed from the surface.
The s in Longines in the first one looks oddly small . ( but that's only from comparing the two above as not my era or knowledge )
Hmmm..... actually it doesn't look so bad but what's most dispositive to me are the "S" on the logo, together with the inconsistencies among numerals on the index track. The highly unusual lack of sub-markings on the index track certainly don't help.
Decisively unusual. Some details make me think about redial, others to originality. It should be examined directly.