The diagram above is for the Type 2 version of the On/On/On mini-switch, as that's the type I usually encounter. If you have a type 1 you just mirror the connections:
You then just connect it as: neck pickup -> mini-toggle -> 4-way lever switch.
The way the 4-way layout works is that the neck pickup's + (hot) is permanently connected to the output of the lever switch and the neck - is only connected in positions 2,3 and 4. This leaves the neck - 'dangling' unconnected in position 1 (bridge pickup only selected) and can potentially act as an antenna to introduce noise, depending on a lot of things. The 'extra jumper' on the 4-way lever switch in the linked thread is intended to reduce this by shorting the neck pickup's + and - together (as a closed loop) on the lever switch's output when in position 1. On a well shielded guitar with the neck humbucker screen/shield (bare wire) connected to ground the effect of the additional jumper may be minimal, but some people prefer to add it.
To include the extra jumper on my layout you can simply add another solder point to connect the first lug on the left bank/pole of the lever switch to its output.