Hmm…the gate walking of the Simon Necronomicon has nothing to do with the Tree of Life or the Qlippoth as far as I can tell. Those belong to the Hebrew mysticism of the Kabbalah, and the Simon stuff is a really bad pastiche of Sumerian mythology (I am assuming you are referring to the Simon book). They are not the same thing.
The Lake of Fire ritual is also not connected to the Qlippoth at all and its only connection to the Goetia is the fact that one of the Gatekeepers is Belial. I don’t think completing the Lake of Fire would make calling those spirits any easier than it is already.
Here is someone’s experience gate-walking using a different version of the Necronomicon: