The driver for Lion is fully functional, the problem more likely somehow related with your envoirnment.
Try the following steps to get the problem sorted:
Step one: Reset the printer system:
Step two: remove any current HP drivers
Go to Computer > Library > Printers and move the HP folder to the trash.
Enter PPDs > Contents > Resources - search for 3050 and move any instance of the 3050A / J611 to the trash.
Step three: Repair the disk permissions
Go to Utilities > Disk Utility and select your active boot volume.
Click Repair Disk Permissions and allow severla minutes till the log indicate it been completed.
Step four: Install the latest software
Download and install the software below, be sure to check HP Recommended Software during the installation.
Step five: Update the drivers
Clcik the Apple icon, select Software Update. be sure to select any listed HP Update and click Install.
Please let me know of any problem,
I can now use the printer. Thank you.
The only (minor) problem I had was with Finder. It wasn't allowing me to see the /Library directory so I used the Terminal program and basic Unix commands to remove the /Library/Printers/hp directory.
(Note: late reply because of holiday travel.)
I followed your advice and it worked for finding and installing the 3054A driver on my Mac with Os X v 10.7.5. However, even though the computer can find my printer through the wireless connection, it will not print. The job sits in the queue looking like it is loading. I did a wi-fi diagnostoc on the printer and it said everything was fine. Any ideas?