Fairscale integration tests for Lite

[awaelchli]

What does this PR do?

Analogous to #14901 and #14815

Before submitting

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• Did you make sure your PR does only one thing, instead of bundling different changes together?
• Did you make sure to update the documentation with your changes? (if necessary)
• Did you write any new necessary tests? (not for typos and docs)
• Did you verify new and existing tests pass locally with your changes?
• Did you update the CHANGELOG? (not for typos, docs, test updates, or internal minor changes/refactorings)

PR review

Anyone in the community is free to review the PR once the tests have passed.
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Did you have fun?

I made sure I had fun coding 🙃

cc @carmocca @justusschock @awaelchli @Borda @akihironitta @rohitgr7