What exactly is going wrong, at what point in the process? You made floppies, but the Lisa wouldn't read them? Or something else?
So you have a Macintosh Classic, and a Mac Mini running OSX, right? How are you transferring files between the two? You mentioned you'd already made some Lisa floppies successfully with the Classic, so I assume you've got some path for downloading files from the internet to the Mac Mini, than transferring them over to the classic.
What software do you already have on the Classic? Do you have ResEdit, or a utility called SetFType, or StuffIt (any version)?
What you probably need to do is download files from the internet to you Mac Mini, and unzip them there. I'm guessing that inside of the zip file, you'll find a .sit file, or a .image disk image file. Transfer these to your Classic.
This transfer process will have lost the Macintosh type and creator IDs from the files, so tools like Disk Copy may not recognize them. You can use ResEdit or SetFType on the Classic to set the type and creator IDs of each file to the appropriate values, then you should be able to view and open them in the other utility programs. I think StuffIt may also have a way to force it to show *all* files when you're browsing for a .sit file to open: a checkbox in the file dialog maybe, or hold down the shift key, or something like that.
StuffIt archive files should have a creator of "SIT!" and type of "SIT!", "SITD", or "SIT5" depending on what version of StuffIt was originally used
Disk Copy 4.2 image files should have a creator of "dCpy" and type of "dImg"