A common workflow is to use Lightroom as your main catalog and library, then send photos to Photoshop Elements only when you need edits Lightroom can’t do.

If both programs are installed on the same computer, Lightroom can open an image directly in Elements. After editing, save the file as a PSD (or similar supported format), and Lightroom will automatically show that edited file in its catalog. This avoids maintaining two separate photo libraries. In Lightroom, the edited PSD can also be stacked with the original RAW file, which keeps things organized.

A simpler alternative is to export a JPEG from Lightroom, edit it in Elements, then import or sync it back into Lightroom. But opening directly from Lightroom is usually the smoother workflow.

So in practice: keep your originals and catalog in Lightroom, use Elements as an external editor when needed, and let Lightroom manage the resulting edited files.