It seems very plausible to attach his quip to Lenin, as the Red October and its aftermath was practically exactly that: take action and see what comes out of it.
It seems very strange to attribute this 'motto' to Napoleon who is often portrayed as far more into planning and strategy and tactics. Well, for most of his career. The beginnings might be a little more like that. And equally coming back from Elba for 100 days also bears a certain resemblance for a fitting description. But then, quotes of spoken words from non-writing military are frequently embellished interpolations, or pure inventions anyway.
Lenin himself wrote exactly this:
Napoleon, I think, wrote: "On s'engage et puis ... on voit." rendered freely this means: "First engage in a serious battle and then see what happens." Well, we did first engage in a serious battle in October 1917, and then saw such details of development (from the standpoint of world history they were certainly details) as the Brest peace, the New Economic Policy, and so forth. And now there can be no doubt that in the main we have been victorious.
Who invented this saying is therefore clearly not Lenin, though very well he may have quoted this on occasion.
But another contender for invention is Yakov Petrovich Kulnev, Russian General famous from the Russo-Turkish-War onwards for extreme bravery:
In numerous publications of the first half of the 19th century he is credited with formulating this saying.
Georg Wilhelm von Valentini: "Die Lehre vom Krieg: Der Türkenkrieg, Band 3"
(Prussian General Staff), Boicke, 1822. (Quoting the phrase from the prior first volume p 309).
From him comes the practical saying (First volume S 309
on s'engage partout, et puis l'on voit!
Apparently this characteristic was repeated during the battle of Battin at the Danube on September 7 during the Campaign of 1809/10.
(Fulltext in French translation: Traité sur la guerre contre les Turcs. Tr. par L. Blesson, in English: Military reflections on Turkey. Extr. and tr. from the treatise on the art of war. By a military ...(seems incomplete))