How can I download lubuntu with nothing more than dial-up?

If you can stall at a local coffee shop or fast-food restaurant for an hour, you can probably download it in that time.

If you have a library nearby, they often have computer you can work on stuff with. You can probably download the iso to a USB in that time.

Last resort would be to buy a USB-stick with the iso already on it. You can do that at the Canonical Store.

If you want to stick with dialup, you can torrent the iso, and it can be downloaded over many days. You can also get the direct link and use wget -c <url of iso>. You can cancel this command and re-run it to -continue the download from where it left off.

See if there's a Linux Users' Group (LUG) in your area. My first copy of Linux I got on a CD from a guy at work; a LUG would likely be able to help you get a copy, perhaps in a similar way.

As an alternative to downloading, you could check local bookstores/newsstands for something like a Linux magazine that comes with a DVD with what you are interested in.