There are many case studies of AWS Lambda's scaling power and its constraints are well documented. The newcomer in the serverless architecture is AWS API Gateway Websockets, and I personally have not performed any tests using this service within a variety of use-cases at significant scale (it's still a new service).

When it comes to migration, it depends on your use-case. A few suggestions which may be helpful:

* Consider your data strategy (much lock-in happens at this level). Most serverless architectures leverage DynamoDB because its design pairs well with stateless compute like AWS Lambda. You can use DynamoDB within all types of architectures.

* Don't use AWS API Gateway specific URLs in your application. Use custom domains. This will enable you to easily swap out your websockets endpoint. Fortunately, there is only 1 endpoint in this architecture, so there is little surface area to refactor.

* Make sure you understand the cost of these serverless technologies at scale before building with them. But don't forget to factor in the reduced labor costs of using serverless technologies.