The merits of deploying a complex Rails app on Lambda are debatable, mainly due to the fact that larger code bases will result in slower cold request times for Lambda functions. For HTTP APIs in general, however, the three main benefits of being operational on Lambda are:

* Paying only for compute time/requests, if the API is not being accessed for a period of time, it's free - on a regular instance, you'd be paying for idle time

* Automatic scaling

* Simple deployment

The downsides include:

* Irregular response times due to cold containers

* Slower request/response cycle due to overhead in Lambda + API Gateway