The Lucan web and mobile applications are built using the Bubble and XANO databases. The application allows users to create an account using a company code provided by their respective companies. Once registered, users are redirected to the onboarding process to familiarize themselves with the Lucan application. After onboarding, users land on the home page, which serves as a perk page, displaying various perks with the best offers. Users can click "Shop Now" to visit the respective websites for purchasing products.