From my own experience Internet Sharing is not, and has never been, as reliable as it should. Connection coming back and forth is a usual behavior of the service, heavily depending on the usage of the machine which is sharing the internet connection.
Apparently, updating to 10.7.4 makes things even worse.
Your messages says it clearly.
Your Internet can not be shared!
It is prohibited to do so by a set up called 802.1x.
Your network administrator(or you) has created the 802.1x configuration profile to connect to 802.1x type network.
That profile does not allow you to share wifi (for security reasons).
If you have access to the 802.1x then you can change that.
If you do not have access:
Try creating NEW Location ! (without the 802.1x configuration).
Under Apple(top left) select Location > Network preferences
In the new Network window click on the Location then select Edit..
Now click on the (+) to add new location (name it)
Now select (add with +)the wifi to use, and add Bluetooth PAN (with (+))
Now go to sharing and Enable Internet sharing with BT PAN.
Do not forget to turn off and turn on the WiFi to enable it.
Best Answer
You can not bridge from WiFi to WiFi. You'll have to connect to the internet via a different port if you want to share the connection. I'm assuming the reason you don't connect to the network directly with your iPhone is some kind of client limit. You could use a Wireless Router to connect to the WiFi and repeat and reroute it. If you use an Apple Airport make sure you disable bridge mode.