Do you require Full Depth Order book or just top of Order Book?
Eikon Data API can allow you to get a snapshot of top of Order Book as explained by my colleague Alex in his replies to this post.
In order to consume Full Depth Order Book or even streaming top of Order Book, you will need to use one of our realtime APIs such as Elektron Message API which is part of the Elektron SDK or the Websocket API.
Note that we will be releasing a newer version of the Eikon Data API in a few weeks time which should allow top of Order Book streaming requests (but not Full Depth order book AFAIK).
I am not an Eikon Content expert, but I believe that for historical Market Depth data, you would need to use the TRTH service - e.g. there is a tutorial on extracting Market Depth data: