Dictionary does not need internet access.
I would do a Restart to see if that fixes it.
Also check to see if it is indexing content: from Home or Library, search for '.' (period) and then see if Text in Books category is enabled in search results. If it is, tap and it will show you number of items still being indexed, and tapping on that will display a list of the items it is still working on. The dictionary will not function for any item that is not yet indexed.
In some cases, a download or side-loaded item is corrupt and indexing will get stuck on it. Removing the item will allow indexing to complete and then dictionary lookups should again work.
Note that content usually gets indexed after any firmware update is installed.
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