I was just illustrating the path along the lunar gateway (LEO -> TLI -> Gateway -> LLO -> surface). Even if you do a direct (LEO -> TLI -> LLO -> surface) route, you still have to go through LLO as you'll need to be able to pick your landing spot and potentially even delay a landing (which is not possible if LLO is not budgeted in).

Actually now that I think about it, if you want to save delta-v, you can get an extra 25% off the TLI leg of the direct route with a low energy transfer using weak stability boundary trajectories. These savings however come at the cost of a significantly longer flight time and far slimmer margins for failure.