In both Online and Lectora 17 you do have the option to Scale the view to fit the size of the device on publishing. This is not exactly what you want im afraid. To work from scratch at a higher size you do have to modify the template. Depending on the template at hand that is not that much work, if you have original assets ( .ai and/or .psd files ) accompanying the template its even quicker and easier to get done… but you will have to do it.
Depending on the template at hand, you could opt to get specific parts of the course ( background images ) out of the course and make the course transparent. Then use CSS to show the background-images behind the course in the browser…filling up all of your screen.
Do show/share the template…who knows more bright ideas might pop up.