How to restore a time machine sparse bundle to a new drive

I am replying to my own problem because it started to dawn on me before I read baltwo's response why I am having problems restoring from Time Machine. I was working on a problem with Apple's Store support team on another issue that is related to using earlier OS's, and this is the context of that response.

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I have spent hours reading on forums both internal and external to Apple issues, and have arrived at the conclusion that the difference between Snow Leopard and Lion is my problem for both looking at past purchases and restoring my entire system from a Time Machine backup.

I could get around this problem but there is one issue. When I access the App store from my iMac and see the Lion App I purchased in December, I only have one option and that is the word "Install". I don't want to install Lion on my iMac. My iMac came with Lion. If I could down load the Lion App to my iMac desktop or hard drive, I could transfer it over to my Macbook and install it there. So, the install has to be changed to download, and if it cannot, then I have to purchase Lion again from my Macbook, and pursue a refund though Apple.

Baltwo from San Diego was the final cap on my issue and I sincerely thank you.

I was trying to do a migration but having problems with the migration utility reading the sparse bundle from the RAID drive. I took your approach of booting from the Snow Leapord disk, and running the utilities / restore from backup, but ran into several esoteric UNIX messages from the kernal with the only interpretable message "Mac OS version not yet set", "shut down your computer and restart again", that didn't work after serveral attempts so I resorted back to an early backup I had made on an external USB drive, and went up stairs to pour myself a drink. I had been working on this problem now for 5 hours. When I came down stairs, I was absolutely amazed to be steering at my Macbook with Lion OS loaded and a desktop. I shook my head a couple of times, and then initialized Time Machine and started the process of restoring from the sparse bundle. Everything came back without any further glitches. My Macbook is up and running again.

If it weren't for these forums where somebody had experiences of these sorts, we would all be banging our heads agaisnt the wall. There are answers across the web. They may not be an exact replica, but there will be sufficient information to point you in directions to find answers, and a great group of people to point you there.

Thanks for your time, your advise and pointing me in the right direction............... Cheers!