When Lenin says capitalism > DotP > communism he means the DotP exists until lower phase communism and higher phase communism

However, there is a point where he talks about a state still existing under the first phase of communism (FPC), we should note though that Lenin makes it clear that the state withers away, just not *completely*. This statement clearly presupposes a drastic withering away

In the text above "marxism in the state" and S&R by Lenin, he talks about Engels take on this, how this continuation of the state is no longer a "political state" as we know it but rather as Lenin put it:

Lenin in this chapter of S&R talks about how this non-political state ceases to be a state as the way we tend to use it. The FPC has in a sense an administrative 'state' and thus workers need administration skills that to a large degree is already conditioned on us by capitalism

As the text above the suggest ONLY when everybody becomes an administrative skilled individual and can independently use this 'state' can full communism fully be established and thus the withering of the non-political state

This is my position on statehood under socialism if one can even call it a state anymore.

To add more to this Lenin actually provides more evidence for this position due to this following page. focus on the highlighted sections if mucho texto.