The general approach to compute something in ATK can be divided into two steps:
1. A self-consistent calculation of the system. This is the "initial calculation" I referred to, and it's always necessary. It produces the checkpoint file (NC file), which contains the converged state of the calculation, or the self-consistent density matrix on a technical level.
2. Analysis. This is where you actually compute things, observables, like a spectrum, the current etc. When you set up the calculation in VNL it might appear that you go directly to this step, but in reality the first step is always involved. And, sometimes it's actually better to separate them, since the second step can be performed independently afterwards, provided you have saved the checkpoint file in step 1.
Therefore, in your case, the work-flow should be
1. Set up and perform the self-consistent calculation of the Li-H2-Li two-probe system, as described in detail in the manual, without bothering to compute any "analysis! quantities. That is, just make sure to save the checkpoint file at a well-known location (say, "C:/my_calculation/lih2li.nc") on the "Self-consistent calculation" tab in the NanoLanguage Scripter, but don't select anything on the "Analysis" tab.
2. Enter the relevant path of the checkpoint file into the PDOS analysis script, and run it.
This is specifically needed for the PDOS calculation since this feature is not offered directly in VNL, but it works very generally too.
Note, however, that the PDOS is not the only thing you will be interested in computing, so you also need to consider how to obtain the transmission spectrum etc. This is easier in a sense, since you can just select them in VNL (and perhaps you have already covered this point). The important thing this discussion adds is to always take care where the NC file ends up, so you can use it later to restore the converged state, rather than recompute it.