DynamoDB vs RDS for a counter store?
Why not something like Redis? (can use it through ElastiCache). Hard to answer this without knowing the operational requirements of this project. Is this data strictly for logging/research, or is it operational (i.e. this "table" is consulted in order to know which lambda to invoke).

Dynamo vs. RDS - depends how spiky your traffic is. Dynamo is very scalable and will give you a guaranteed throughput. But if you traffic can grow 10x over hours (spiky) Dynamo might be too expensive, since you'll need the maximum throughput provisioned or else you'll get throttled.

RDS is basically managed RDBMS on an instance type that you choose, so it can handle larger spikes, but ultimately not as scalable as Dynamo.

Again, I would consider Redis, for it's simplicity (seems like you just need a KV/counter store), and incredible speed/efficiency. If it's just for logging, it's probably good enough.