As counterpoint, my C5580 has worked flawlessly under all versions of 10.6 since we bought the unit nearly 2 years ago. Scans and disc printing are normal as well. I wish I could use it via AirPrint connected to my APExtreme router, but it's a known problem that under that setup the scanner will not function. And Ecomm's Printopia is a perfect replacement anyway 🙂
Now, I've kept it updated with HP's latest drivers via OS X Software update, so maybe that's why it works for me.
Will assume that all the major manufacturers will have updated driver packages inside 10.7, since final developer builds have been around for more than a couple of months. If history with 10.6 in August 09 is any guide, it's the very old printers that will suffer problems under the new OS when released - but anything in the past 3-4 years is likely to be included in the launch drivers.
However, with Rosetta support being dropped from Lion there is no way any of HPs legacy printer apps will function and it is highly doubtful that they will come out with any replacements since the existing ones are already 4+ yrs old and did not see any updates from 10.5 to 10.6. We had a Photosmart 7560 before getting the C5580, and used HPs software back then for the 7560 under our Windows setup.
OP may want to spend some time investigating the print/scan capabilities of both Preview and iPhoto, which are reasonably robust and offer many similar features to the HP software - I never found much that I had to have from HPs software but missed under OS X.