I am trying to get the CostCenter, MainAccount and Department starting from the LedgerDimension field in the LedgerJournalTrans table.
I found this but I am lost.
http://ax2009developer.blogspot.ro/2014/02/how-create-customize-look-up-for.html
In fact, for this task, I have implemented only queries in AOT. Is there any way to join some tables and get there without taking the X++ approach?
Financial dimensions in AX 2012 are far more complicated than in previous versions.
You should start with this white paper: http://download.microsoft.com/download/4/E/3/4E36B655-568E-4D4A-B161-152B28BAAF30/Implementing_the_Account_and_Financial_Dimensions_Framework_AX2012.pdf
You'll find the tables involved and their relations.
By the way, I recommend you not to build your own queries. As the model is really versatile, it will be first tricky to build your query, then they will not be performant.
You need to use the APIs as they are already built and also as they use the system global object cache to cache data, as the model is not set for fast queries.