Ran into exactly the same problem with Lubuntu as I did with Ubuntu - the free space on the 4gb drive disappeared as soon as I started to update programs etc. It also showed some weird quirks e.g. icons disappearing from the task bar, and I've decided I just don't like the Chrome browser, and there wasn't room for Firefox.
What I've ended up doing (hopefully as a reasonably permanent fix) is install Linux Mint version 9 (which will be supported for the next year or so) rather than the latest version, and hope that sooner or later I will figure out how to do an install that uses the fracking 16gb drive which actually has some space... It's a version I like, and it was rock solid on the small netbook the Asus is replacing.
Meanwhile, is there any way I can move my home folder at least to this drive, and set things up so that programs will know to use it?