I’m wondering if Lambdas and DynamoDB would be competitive to this setup.
Depends, but it's important to know the details.
Lambdas are used for 2 things in AWS:
1) Glue for managing services and events. (Required for advanced AWS mgmt.)
2) User applications. Lambdas have improved over time, but initially had all kinds of limitations (startup time, database access, 15 minute job limits, etc.)
DynamoDB has also improved a lot. Initially hot keys could cost you a lot of money. Some companies have designed their applications to use it in a way that absolutely no administration is required, reducing DBAs and Ops people.
Source: DBA.