Building react web application on Lambda

Trying to run an entire React web app on Lambda will make for complex code and will likely get out of hand quickly unless it's very basic. You'd also have to consider other aspects like cold starts and concurrency limits and how this affects performance.

A more common and much more easier way is to host your frontend files on S3, and your backend/server-side rendering components on Lambda. Check out this blog post for a detailed example.