The LAV Box was only available in Japan, as far as I know, as it doesn't seem to have been carried by any of the US dealers who usually sell HAO's well-respected overdrive and boost pedals, such as the Rumble Mod and the Rust Boosters. It's described in various sources as a Loop, A/B and Volume effect (thus LAV).
The instructions (included) are in Japanese, but the diagrams are easy to understand. The functions are ...
Loop: To connect an effect or series of effects to the LAV's true bypass loop, connect the LAV's SEND to the Input of the effect (or first effect in the series) and the LAV's RETURN to the Output of the effect (or last effect in the series). In bypass mode, your guitar signal will go through the LAV's IN and OUT with no loss or coloration of the signal. When you step on the LOOP ON/OFF switch, your guitar's signal will pass through the loop before traveling to the LAV's OUT, and the pedal's LED will light up.
A/B: The LAV can also be used as an A/B switcher to send your guitar signal to two different destinations (e.g. two amps, two effects, etc.). Connect the LAV's SEND to the input of one destination, and the OUT to another. When you activate the LOOP ON/OFF switch, your signal will be directed through the SEND output to the destination at the end of that connection. When in bypass mode, your signal defaults to the LAV's OUT line.
Volume: To use the LAV as a pre-set volume pedal, use the included attenuator cable to connect the LAVs SEND directly to the RETURN jack. In bypass mode, your regular input signal will be unaffected, but when you activate the LOOP ON/OFF switch, the signal sent to the OUT jack will be reduced by about 30%. You can use this as either a "solo boost" (by keeping the LAV switched ON and then stepping on the bypass switch for an instant volume boost), or as an automatic volume cut for quieter passages.