The unit you need is a 4-channel version of their TCIP4 (they come in 2 and 4 channel versions). Just tell them what it's for and they'll pre-load it with suitable software.
Also tell them what pickups you're using. Their units use different internal hardware (or firmware?) for Hall pickups than they do for VR (magnetic coil) type pickups, so you need to specify at time of ordering.
If you also buy the basic wiring harness for the TCIP4 (multi pin plug with wire tails pre-fitted), it saves a bit of fiddly work crimping wires onto the connectors and inserting them into the plug. That's especially handy if you don't have a crimping tool for the small connectors in the plug. If you buy the pre-wired harness, I'd suggest you remove any wires that you don't use to make the installation tidier. The cable connectors are easily removed from the plug with a suitable pointy tool to release the little catch that holds them in.
The guys at Ignitech are pretty helpful. They'll tell you what you need. They've done systems for Laverdas before.
Alternatively, you could buy Red's plug-and-play ignition upgrade kit for 120° Laverda triples. It consists of Hall pickups and rotor, and an Ignitech module pre-programmed for your bike. All components are very nicely made, and it comes with comprehensive instructions.
You can contact Red via the forum (redax5)
https://www.laverdaforum.com/xf/members/39/
or Facebook
https://www.facebook.com/people/Redax-Laverda/100063710341535/