Serverless Architecture – Integrating with Data Layer

My question is in context with the Serverless Architecture (e.g. AWS Lambda) and how does one interact with the Databases in this system.

Typically in a 3 Tier architecture, we have a web service which interacts with the Database. The idea here is to ensure that one database table is owned by one component. So changes in there, does not require changes in multiple places and there is also a clear sense of ownership so scaling and security are easier to manage.

However, moving to serverless architecture, this ownership is no more clear and exposing a web service to access a database and having a Lambda use this web service does not make sense to me.

I would like to know a bit on the common patterns and practices around this.