Any one know about Wi-Fi and iPad

Just so that I'm clear, are you connected to the Internet on the iMac via a wired connection? Can you confirm that you are able to connect to the Internet successfully on the iMac?

You know, a thought just occurred to me. Is your iMac connected to a modem or a modem-router? For example, if the modem has several Ethernet ports on it so that you can connect multiple devices then it probably is a router. The importance of this is for answering the question, what is assigning IP addresses on your network? What I am thinking here is that your modem is just that, a modem, and that the IP address your iMac is using being assigned by your ISP. Some ISPs only assign a single IP address so if you want more (such as one for your iPad to use) then you either need to buy another from your ISP or invest in a router (or modem router) that can assign IP addresses using its own DHCP server. DHCP is what your iPad is trying to use - it's asking the iMac to assign it an IP address and it looks like that isn't happening. What may be happening next is that your iMac is passing on the request to your ISP and your ISP also isn't responding to that request.

I seem to recall having a similar problem with an ISP years ago.

I hope I'm barking up the right tree here.

No, I don't think so. Each device should have a unique IP address else messages to/from devices may be delivered to the wrong address.

That sounds unlikely. If you were trying to connect your iMac to your iPad then I don't think your iMac would be able to connect to the Internet.

OK, I'm going to try doing this myself and see what result I get with an iPhone and my iMac (also running Lion). It is possible that this issue is a Lion issue since you seem to note that prior to Lion all was OK. I'll let you know what result I get but this will probably take an hour or so.

OK, that was all very instructive. Basically, this seems to work fine for me so what we ought to do is see what is different for you. To do this I'll walk you through what I see and you can say if you see something different.

1. My iMac is connected directly to my ADSL modem/router. The modem/router is assigned a public IP address 95.***.***.52 by my ISP (sorry, I'm masking part of my IP address for privacy). I can see this by connecting to my modem's setup software, which I access using Safari and the modem's IP address (in this case 192.168.2.1).
2. When I open System Preferences and select Network my Location shows that my iMac is connected via its Ethernet port. The Ethernet port shows that Configure IPv4 is "Using DHCP", my IP Address is 192.168.2.2 and Router is 192.168.2.1. Everything looks OK and I can connect to the Internet.
3. To allow my iPhone to use the iMac's network I opened System Preferences and then Sharing. From the list of Services I selected Internet Sharing, ensured that the connection to share from was Ethernet and selected Wi-Fi as the connection to share to. For security I selected Wi-Fi Options, choose 128-bit WEP from the Security menu and set a 13-character password, plus made a note of the Network Name. Having set things up and returned to the Sharing screen I could now select the Internet Sharing checkbox to start sharing the Wi-Fi connection.
4. On the iPhone I opened Settings and selected Wi-Fi. From the list of wireless networks in range I choose the name of the network as was setup in the Wi-Fi Options pane on the iMac. The iPhone requested me to enter the WEP password that I setup, which I entered and the iPhone connects to the Wi-Fi network after a few seconds.
5. Again on the iPhone's Settings Wi-Fi screen I can see that the name of my iMac's Wi-Fi network is selected. By tapping the blue arrow on the right-side of the screen for that network I can see more details about it. The screen displayed shows that my iPhone is using an IP Address assigned by DHCP, has the IP Address 10.0.2.2 and is connected to Router (the iMac) 10.0.2.1.

So, in my case the modem/router has an IP address (95.***.***.52) assigned by my ISP, the iMac has the IP address 192.168.2.2 assigned by the modem/router, and the iPhone has the IP address 10.0.2.2 assigned by the iMac. In effect there are 3 networks here.

That sounds to me as though you are currently looking at the File Sharing option in Sharing. What you need to select is the Internet Sharing option, which is displayed towards the bottom of the list of services in Sharing, unless I have thoroughly misunderstood your requirements.

To clarify, the File Sharing option enables computers on the same network to connect to your iMac in order to (*shock*) share files. The local network address that you are quoting is what you would enter into the Finder on another computer (via the Go > Connect to Server option, I think) in order to connect to your iMac. This have nothing to do with connecting your iPad to the Internet and is not what you want.

My apologies, I see that the local network name for your computer is displayed when the Internet Sharing option is selected as well. The point remains, however, that this is completely unimportantant for the subject of creating a Wi-Fi network from your iMac that will enable your iPad to connect to the Internet. For the record, my Sharing panel looks like the following.