Hi @vainkop 
Do I understand you correctly that you wish to run a hybrid setup as follows:
Kinesis (LocalStack) => Lambda Event Source Mapping (LocalStack) => Lambda function (AWS)
You want to run Kinesis locally, let a local Lambda Event Source Mapping poll from the Kinesis stream, and finally invoke a Lambda function that lives in a remote AWS account, correct?
Could you share your use case to help us understand why you wish to use such a hybrid setup?
It helps to improve the developer experience of LocalStack 
We currently don’t have a blueprint or tests for this exact scenario. However, it could work using our experimental AWS Replicator Extension . The replicator extension can be configured to forward the relevant Lambda lambda:InvokeFunction call using an ARN filter for your specific Lambda function. The “proxy” Lambda function in LocalStack needs to have the same ARN as the one in your target AWS account.
The reverse case (local Lambda & remote source) is discussed in Local Lambda against remote SQS? and @HarshCasper from our DevRel team has created resources related to this use case:
- Replicating cloud resources locally with LocalStack’s AWS Replicator extension | Docs
- https://youtu.be/wSFN3oJbYrk
Looking forward to hearing your feedback 