Instead of using an application to convert your files, I suggest you use an online service. There are plenty of these services which you can use to convert your files. In this case I recommend using Convert.Files online service. I have tested the service and it works flawlessly and I had my file converted in a matter of seconds. Since I don't have a LIT file, I have used a PDF file and converted it to EPUB.
If you want a software solution, I suggest you open your LIT files in any supported program you use and then use the PRINT function after you install CutePDF Writer. This application is a virtual printer which allows you to export all kind of documents to PDF format. Instead of the actual printer, you need to choose CutePDF Virtual Printer and that's it. Your files will be converted (printed virtually) to PDF.
