We are using AWS elasticache service and trying to test our application in case of replica lags. Since Elasticache nodes are in our private subnets, I thought that I could add deny rule to master node's subnet inbound section and introduce replica lag to my test elasticache cluster. I could not succeed till now. Is that scenario possible?
No, it's not possible. You don't have control over the communication between the ElastiCache nodes and you can't define security groups / network ACLs to limit it.