UPDATE: changes in the Windows 10 Anniversary Update
Many would know that loading and/or saving puzzles and games with Lode Runner Online: The Mad Monks' Revenge under Windows 7 and 8 was problematic. A fellow Presage Lode Runner fan has instructions on how to get MMR to work with vaired results. If you haven't already done so, visit his blog and read how.
The good news is that if you have Windows 10, you can save and load games and puzzles. The save dialog doesn't have a textbox to specify a file name which means saving is a little trickier. As a workaround, navigate to a folder that has saved games or puzzles, make a copy and then rename the file to whatever you want (just use copy/paste/rename from the dialog). Select your file, click save and overwrite it when prompted.
How to save in Windows 10
Of course, you are more than welcome to download my rewrite and enjoy the look and feel of the original but with full support for Windows, Mac OS X and Linux ;)