You cannot compile single files, only projects.
A project [.csproj] is a "container" (it doesn't actually contain files, it just points to them) for the C# source files [.cs] and all other files that belong to your project (images, etc.). It also has a certain output type, either Windows/Console Application [.exe] or Class Library [.dll], which defines what the result of a successful compilation is.
A solution [.sln] is merely a "container" pointing to different projects, so that related projects can be grouped together.
So what you want to do is, open either the solution or project, then locate the file you want to modify in the Solution Explorer (should be a tab on the right side, alternatively View > Solution Explorer). Open it and modify whatever you like, unless it already has the modifications, of course. Then go to the Build menu and select Build Solution (or equivalent, whatever is available. I think F6 is the shortcut). This will generate a new output in the "Debug" or "Release" subfolder of the project. Navigate there with normal Explorer, then replace whatever file the Lapper application is (I guess some .exe?) in the directory you installed Lapper to and try out your changes. Don't forget to back up the original .exe though, just in case you screw up.