I have two applications, APP1 and APP2, using Java RTI DDS 6.1.2. Each app operates in a separate domain. There is a specific Liveliness topic (let's say LivelinessApp1 and LivelinessApp2) with a data type of keyedString created so that each application publishes its name, and it can be identified and detected if it's alive or dead.
A routing service (more than one) will be added between them. I created two routes for each liveliness direction, and everything works without issue.