kiamatthews: I bought the same LG monitor for my daughter's MacBook and I couldn't get it to work. Then I read your post and resigned myself to buying the mini-dvi to VGA adapter. Luckily, I stubbornly tried one more time and after a bit of fiddling I finally succeeded in getting it to work. (My daughter has the same setup as you i.e. LG W2252TQ LCD monitor connnected to a MacBook using the mini-dvi to dvi adapter and a dvi cable connected to the monitor.) I'm a relative newbie to Macs, so I'm not sure I've remembered all the steps, but here goes.
When I first connected them, the LG showed the background from the MacBook, but nothing else (no icons, no windows, etc). Eventually I brought up system preferences - displays, and some sort of monitor resolution window appeared on the LG, but it was different than what was on the MacBook. The "displays" window on the MacBook did indicate both the MacBook monitor and the LG, which it showed as 2252TQ or something like that. Anyway, I checked a box labelled "Show displays in menu bar", which then put a monitor icon on the menu bar. When I clicked on that, there was a line allowing me to select "mirror" which I did. Immediately, what was on the MacBook display appeared on the LG. After I picked myself up off the floor, I was able to change the resolution for the LG to its maximum setting and after about 2 seconds of blank screens, it reappeared with everything working as it should.
I hope that the above description is sufficient to get yours to work as well.