How do you handle distributed locks when your system needs to process a ton of requests really fast?

Hey everyone, I'm trying to figure out how to implement distributed locks for a system that has to handle tons of requests all at once. We've been thinking about using things like Redis locks (Redlock is one example) or ZooKeeper. But, I'm worried about them slowing things down or breaking. What have you guys found when using distributed locks for stuff like this? Are there other ways or tips I should know about to make sure it's correct and always available, even when things get super busy?