Can I restore from a volume created from a Time Machine backup?

I had to replace my hard drive. The new drive had Snow Leopard and before I restored from Time Machine, I upgraded to Lion, which I had before. I went to Time Machine and selected the the latest backup file and hit the Resore key. It created another volume on my hard drive and all the data is there. However, this is not what I expected - I thought it would retore the computer to its last state.

I read I can't retore the whole system by hitting the Restore key in Time Machine. I should have used the Migration Assistant. Question: should I delete the volume Macintosh HD (see screenshot) and start over or can I restore from this volume?