Is there a way to create a link connecting an icon in our lobby directly to the sport in the iFrame?

This can be achieved with the ROUTE_CHANGE event functionality as described in our iFrame documentation. You should listen for the ROUTE_CHANGE event when you browse the iFrame, where opening a unique or filtered page (for example, by sport or tournament) will produce a unique route name. You then insert the route name in the URL pointing to the page where the iFrame is displayed, for example: https://bet.bet/esports?page={route_name}. This URL can be used as a direct link to the selected unique or filtered page.