I'm running LR from the smallest size Acer Aspire One netbook. I'm using it mainly as a review and storage platform in the field. I upload everything from my cards to the Acer via LR. Then I can delete the obvious flubs, add keywords, make labels and captions etc. I store all that on an external drive so that I can plug it into my main desktop machine at home, and just open or import the field catalog. Is it the optimal solution for editing and retouching? Of course not, but then again my tower won't fit in my camera bag.
I'm dual booting two different OS versions on the Acer; Windows 7 and OS X. It turns out that the Acer uses very generic Intel hardware, so it's easy to get OS X running on it. In OS X, you can type a simple command which scales a window up or down in resolution. That neatly solves the import dialog box sizing issue. Again, it's not a prefect solution, but it works reliably. I got the Acer for $200 as a refurb at CompUSA, so you can't argue with the price.
Before anyone gets huffy about running OS X on a PC, I bought a brand new retail copy of Leopard 10.5.6, and I'm running clean, legal licences of all the applications I'm using on it. I'm probably violating the Apple EULA, but I'm not depriving anyone of the money they deserve, as Apple doesn't make a netbook. And I did buy one of those snazzy aluminum bluetooth keyboards to use with it.
I also have a large external monitor at work. Both OS X and Windows 7 drive it just fine, at full resolution. When Windows 7 detects it, it switches the primary display to the external monitor, and uses the netbook LCD as the secondary. OS X won't do that, but it does work like any dual screen setup otherwise.
So I'd say LR is very workable on a netbook, within limits.