You could either open and re-save your models or use the Monarch Utility and choose the option to "Manage external references in binary models or projects". The wizard will let you specify the location of your models/projects and update references to database connections and external models.
Hope that works.
Where are the external lookups in your network?
Are they on the same (new) server?
The lookup values are added to the table from where they will be derived for use n Summaries where indicated.
Are all of the lookups external or might some be internal?
If you look at the model information do the lookup locations offer any clues about where the issues might be?
Are you running the process as a project?
Have you assessed whether there might be any network performance delays for any reason?
Just throwing up some ideas.