When you write "your live stack", my brain freezes. Even a simple "webapp" project in my team had 4 common stacks (prod, staging, dev, git-master which had every push to master getting deployed) plus individual stacks, one per developer, with the ability to create extra stacks for specific feature development.

Only prod had real data. Obviously (to me) you wouldn't shorcircuit lambdas in the prod env. Not even staging. Not even dev. Not even git-master. Short-circuit development environments where you explore. Very low risks there. We need to learn it's ok to fuck up, as long as we fuck up in a safe environment, nowhere near the nuclear button ;)

Just create a staging env, if you don't have it already, and point to staging