... L.W.W. stands for "Longines-Wittnauer Watch" Corporation. They were the importers for LeCoultre back then. JLC made the movement in Switzerland and LWW made the case in the USA.
Some of the early models didn't have the Cased and Timed, etc. engraving inside.
With pictures, it would be easier to give an opinion.
Take care,
gatorcpa
...may be engraved underneath or near the balance wheel. I would be wary if dial seems too clean. Could be a re-dial. Case and dial condition should match. It's an old watch, it should look like it.
Again, without pictures, it's very difficult to assist.
Good luck,
gatorcpa