The original disk brake was cable operated and had a static inboard pad and a operable outboard pad. The disk in the center of the hub was able to slide on three pins and the outboard pad would push the entire disk until it was clamped between the inboard and outboard pad. These hubs can be retro-fitted with a hydraulic piston in the place of the mechanical system. A detailed disassembly page of the standard disk hub can be found here.
Over the years many people have borrowed motorcycle parts and fabricated outboard disk brakes for Lambrettas. In the last couple of years many shops have started to offer kits to convert a standard front drum brake to a full hydraulic version. Below are a list of some (but not all) of the shops I know of offering full conversion kits.
The sexiest kit is available from MB Developments in the UK. This kit is the sexiest one I have seen and has a beautiful aluminum caliper bracket that can be polished to an almost chrome shine. The detail is truly beautiful, and even the speedo drive is incorporated into the one piece cast bracket. It runs around £400 for the full kit but check with MB for final pricing.