Using lightning.force.com/lightning in a URL link should be enough to have the user's page opened in Lightning Experience (LEX).
In terms of opening a specific app, I've queried the DurableId of the AppDefinition I'm interested in and a link format of:
That should then ensure it opens up in LEX with ...
Look at the Dashboard metadata.
With VS Code and the CLI installed, you can run the following command in the terminal to retrieve all dashboards
sfdx force:source:retrieve -m Dashboard
Otherwise, you could use the following package.xml and workbench to retrieve the dashboard by developer name.
<?xml version="1.0" encoding="UTF-8"?>