I susequently purchased a new imac 2.9 intel core i5. My old imac had an external hard drive to which I backed up. Unfortunately, the new os, 10.9.2 does not recognise the back up which used the lion os. As a result I cannot access my previous files. Can somebody advise me as to a solution please.
Take a look at > OS X: How to migrate data from another Mac using Mavericks
In your case you may need to use "Copying your Files" using an external drive, which is half way down the following > OS X: Manually migrating data from another Mac article.