Admittedly, I know nothing about LG phones - I won't be able to help there. The one thing I can tell you is to make sure that you don't download the ZIP archives, only download the MP4 files directly from each lesson. I don't know of any smartphone that can handle a ZIP archive because it has to first be unzipped and stored on a local file system. Many phones have a local file system, but it's hard to find an app to navigate them and they aren't consistent from phone to phone.
I can, however, view the course via the browser in my phone by logging into the member area - that seems to work for me using an Android phone and I've tried it on my ipad to confirm it works with iOS. I don't know what OS your LG uses.
I've logged in to the member area from both windows and mac computers, using various browsers, and confirmed that I can view all of the videos and navigate around the member area correctly using the links provided on the page.
I am happy to try and figure this out if I can. I need to know more details about which file you are trying to download (on which page) and if you can tell me what type of computer you're using and the browser/OS that would help as well. Also, what player do you use to play the video files once they are downloaded?