We have some measures in place on our node. Bigger instances are certainly going to want to have some solid network monitoring tools in place and DDoS protections.
We can't really mitigate this at a network level for users in our product, but what we can do and what I've been thinking about is how to most easily let users do backups, restores, and distribute justice transactions as swiftly as possible.
While most fears about these sort of things should be assuaged by reasonable timelocks on your channels, there's still a bunch we can do to make casual end-users feel reassured