Great that you could make it work, Robert. You start Lightning on your client machine(s) and also on the host, i.e. the machine that runs Bryce to include it (though this is not mandatory).
In Bryce, File > Render Animation. A window opens, enable Render on Network on bottom left, then click on Configuration. Yet another window opens. Search the network, it will take half a minute or so. You will get a list of clients. Hopefully, they have green buttons. These change to amber if the respective client is crunching numbers. If you render a still picture, enable Use Tile Optimization, if it is an animation, each frame is already a tile and using Tile Optimization makes the render longer. For stills, a tile will be 100 by 100 pixels.
Ok out of this window, in the remaining window, set the file format as BMP by clicking on the down arrow next to Output Module, then Set the File Location. Ok out of this window. The render will eventually start. The whole source file is sent to each client, one by one, and each client who got the file signals that it is ready. The host will then send it the first tile.
You can watch the progress in the File > Network Render Manager. Hope this will get you going. (Render Animation for a still render on network is a bit confusing, I know.)