After I use PureRaw to denoise, I want to import that image into LightRoom. Is the recommendation to export into DNG format or what?
Yes because DNG preserves the advantages of Raw file processing, particularly enhanced dynamic range and color control. JPG loses information. TIFF files aren’t really Raw files and are much larger. Lightroom Classic treats these DNG files like camera Raw files, which is what you want for maximum flexibility in editing.
The workflow options when using PureRAW with Lightroom Classic are described on pp. 99-106 of the PureRAW 6 User Guide which can be downloaded here: PureRAW Guidelines – DxO PureRAW
Import your Raw file first into Lighroom Classic (I’ve never Lightroom “in the cloud” and have no advice on that one if that’s what you use), but in Lightroom Classic, highlight the image(s) you want to use with PureRAW, and go File > Plug-in Options > Preview and Process with DxO PureRAW 6 to start, exporting as DNG. As you get more comfortable with PureRAW and your settings there, you can switch to one of the other more direct or instant options that skip the preview in DxO if you prefer.