Hi there, when i open up my 2gang and 3gang mechanical switches, i too face similar issue as u.
There is this bridging wire between my two Live wires. I guess the current is pass thru this bridge to other Live wire so that it can power up other switches in bedroom for example.
So watever u do, just rembr to retain the current 'linkages' between the switches. What I did is to connect both the Live wires in L hole, and i can remove the bridge wire since now both Live wire touches in the same L hole on the switch.
U mentioned u hav another bridging wire between your two loads? Not sure if i read correctly, if dats the case u just put the separate wires to respective load holes(your L1 & l3 according to pic) and then the bridge wire to connect both loads as per existing concept if it was connected like this in your mechanical switch? Then u can try it out. Not sure if u get what i mean.
Disclaimer: i trial and error my own switches and is not a professional electrician, if in doubt, best to get a professional. Safety first.