how do i use a dead letter queue for aws lambda errors?

The reason why your DLQ does not work is because using Test button or invoking function using:

aws lambda invoke --function-name testFunction --payload '{"desire":"error"}' /tmp/out.json

result in synchronous invocations, rather then asynchronous ones.

To invoke your function asynchronously, you have to use Event type in the CLI:

aws lambda invoke --function-name testFunction --invocation-type Event --payload '{"desire":"error"}' /tmp/out.json