To summarize:

Yes, you can "transfer this customization to another project in a different server".
But you cannot do it with a single operation on the lifecycle project area (LPA), but rather have to do it separately on each "artifact container" in the LPA. (where RTC, RQM, and RRC effectively each have an artifact container, i.e. the CCM, the QM, and the RM artifact containers, respectively).

So that means that to create a similarly customized LPA on a different server, you separately create each artifact container, create the LPA itself, and then link the LPA to each of those artifact containers.

The other answers in this thread go into details on how to export the customizations of an artifact container from one repository to another.  To summarize, all artifact containers support an "export/import" sequence (which effectively lets you export key aspects of the artifact container out to a file on disk (usually called a "process template"), and then let you import that file to initialize a new artifact container (either in the same repository or a different repository).   In addition, both RTC and RQM (not RRC) allow you to have a new artifact container "share" the process (including customizations) of another existing artifact container (in RTC/RQM 4.0, you can share across repositories, while previously, it was only within a single repository).

Note: There is such a thing as a "lifecycle project template".   When you create a new LPA, you get to select which template to use.   What does not yet appear to be the case is an easy way for you to create your own lifecycle project template, but there is a work item for it: https://jazz.net/jazz/resource/itemName/com.ibm.team.workitem.WorkItem/154368
There is also a work item for documenting how to do this by hand: https://jazz.net/jazz/resource/itemName/com.ibm.team.workitem.WorkItem/127944
but that work item isn't scheduled either.

No, export/import of projects is not possible today for any of the applications mentioned above. Neither across servers or on one server.

As mentioned above it is indeed possible to create customized templates for LPA projects.

You can also build LPA projects from existing projects.

Hi Shirley
Yes you can actually export the process from one project area as zip file and it can be reused across different project area

In the overview section of the project area admin page , there is option to choose from:
Do not share the process configuration of this project area
Allow other project areas to use the process configuration from this project area
Use the process configuration from another project area for this project area

Once you share this process, it is available to be used by other project area as you can see last option

I suppose the question is what is "Export/Import" of a project, and which application.

It is true that there is no CLM wide export and import and with the RRC  process template no modifications should be made, however it is possible to export the latest version of the artifacts (without comments, history, reviews, suspicion, access control nor CLM links), artifact types and links as a project template. The  Money that Matters sample, JKE Banking project is one such RRC project template used in creating new projects.

Project Templates:

• Can be used to copy project templates to other servers, such as from a staging server to a production server.
• Useful for future projects you create in the requirements management application.
• Can be created and modified using an existing template.
• See Creating templates for a list of items that can be included or excluded in a template.
• Useful for sharing standard custom project templates that are applicable to other repositories.
• Can not be used as a project backup as artifact history, comments, reviews and access controls are not preserved. Also does not preserve links outside of the artifacts in a template.

There is also ReqIF for exchanging some (with limitations) of the requirements (across RM servers and tools):

• Used to exchange requirement artifacts and associated metadata between software tools from different vendors, including Rational® DOORS® products.
• See ReqIF for a list of supported and restricted data.
• Does not currently support "roundtrips" (updating existing exported artifacts). Every time you import artifacts, new artifacts are created in the repository.
• The ReqIF specification provides a means for tools that implement this specification to exchange requirements information.

In addition to Pramood's comment, you can import the templates into to tools and create a new life cycle project template that uses the templates. Export the LPA template's XML, edit it and upload it with a new name.

Process sharing is a great way too. For that you would use the uninitialized process template(s) in the lifecycle process application template. After creation you would point to the sharing process. Process sharing is a bit limited for RRC today (only roles) for technical reasons. Process sharing today also limits what you can do in the projects that share. If you configure the process in a project area that shares, e.g. adding a work item, the whole area is copied over into the sharing project area and not shared anymore. Updates in the shared project area will be invisible to the overwriting project.