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You don't need 10.6 because you are running a newer Mac OS X version and because your printer is supported in Lion > http://support.apple.com/kb/ht3669#HP
As it looks like you want to set it up wirelessly, follow these steps to add the printer to OS X > http://support.apple.com/kb/HT4670 You don't need any driver for wireless printing, but OS X will install the printer driver to work with the scanner
What computer do you have? Snow Leopard, 10.6, requires an Intel processor. Go to the menu/About this Mac and it will tell you the processor. Here are the requirements for 10.6.
Mac computer with an Intel processor
- 5 GB free hard drive space
- 1 GB RAM
- DVD drive for installation
If you have an Intel processor, you can go straight to 10.6.
If you have Lion as you mentioned (OS X 10.7), your system meets the system requirements for the printer,
Try installing the drivers below and check if that may help getting the issue resolved: