First of all, the question, as it is, makes no sense at all. Lightswitch is nothing but a Visual Studio version, and Visual Studio is nothing but IDE. It does not build any projects, it provides the UI front-end for doing this work:
http://en.wikipedia.org/wiki/LightSwitch#Visual_Studio_LightSwitch_2012[
^].
As all IDE, the Visual Studio application is interactive. It requires that someone would be able to hit all those keys, depending on what's presented on screen, and so on. Who do you think would do it on the server side? (Do you have to explain that ASP.NET is a server-side technology?)
However, it does not mean that the idea of such functionality makes no sense. You can really do different thing: you can create the Web application imitating Visual Studio. Actually, this is quite possible, and I don't even see any major technical problem. The only problem is that this would be a huge work, even greater work that the one done by the Visual Studio team. However, you could create highly scaled-down version. Come to think, you have everything to do that. First thing to understand is this: Visual Studio is absolutely not required for development, this is just a highly convenient tool. All the development can be done on bare (freely redistributable) .NET Framework. Of course, you can edit all files using some HTTP editor, even with syntax highlighting. But how to build? Everything comes with .NET Framework: MSBuild and two compilers: C# and VB.NET. You can use them in any .NET application (including ASP.NET application) via CodeDOM:
http://msdn.microsoft.com/en-us/library/y2k85ax6.aspx[
^].
That's all. Care to try? :-)
—SA