The strength to overcome capitalism has to come from somewhere, doesn’t it? Lenin says that for the workers to achieve this strength, the organization of the working class is necessary,

So far, so good.

because it is the only weapon we have in front of the entire state apparatus that the bourgeoisie holds and the only way to organize this force is through a vanguard party

See, this is where it runs into problems. The whole idea of the vanguard party ignores that this vanguard, if successful, is placed into exactly the same position as prior (usually feudal) elites, and that material conditions thus suggest that a similar relationship of the vanguard with society will come about - which is what has happened every time thus far.

I'm more partial to syndicalist notions, personally.