Copying Apps with Cross App Relationships

I don't think it's possible. but something that can help you if you ned to rebuild the relationship is this.

 Look up field is just a connection between a reference field in a relationship and the field do you want to look up from the parent.

You can edit any lookup field to attach it to the new reference field from the new relationship and save.  Then immediately edit  it agains ands be presented with the new list of available fields to look up.

While the process is still manual this allows you to preserve the field in your database which is no doubt used in many reports, formulas, forms and even subsequent lookups. So that way you don't have to actually delete any fields and replace them, .... you just redefine the Relationship connections for that field.