Yep, I have this set up and have had no difficulties whatsoever. You received your Licence Key No. from Topaz and have fully downloaded and activated i guess (to a Photoshop program, not Lightroom). Thing is though I didn't think that it is a plug-in to Lightroom exclusively.
I have mine on Photoshop Elements 10 and have to go there from Lightroom to utilise it.
I am not an expert on this but my set is Lightroom 3 (and 4 beta) Photoshop Elements 10 with Topaz Plug ins downloaded there.
Hope I have helped a little (maybe
)