Not sure this is the best way but here's 3 methods I would try.

A) If your machine has access to client data source

1. Add client's data source to your process
2. Add rights for the process to see that data source
3. Go into the lookup rules for the process and change data source to point to the new one. (Rules should stay the same.)
4. Export the process
5. Ensure client data source is setup in Forms
6. Import the process
7. Ensure the process has rights to the data source.

B) If customer machine can access current data source

1. Log into the customer forms application and add the datasource you are currently using
2. Add the new data source to the client machine
3. Export your Forms process from your machine
4. Import your Forms process to the client machine
5. Add rights to the process to use the new data source
6. Go into the Forms process and change the Lookup Rule, available sources, to point to the new one if it isn't showing up already.

C) Another method (If client machine can't point to your current data source)

1. Add new data source to client machine
2. Export process from your machine
3. Edit the xml file where references to <externaldatasource> are made and change values to the new data source (little messy but definitely workable)
4. Import the process to client machine
5. Ensure the process has rights to the datasource in the datasource menu.

*Removing any datasource which existing lookup rules use will instantly remove those lookup rules.