The lambda execution is not suspending and the lambda container has no port exposed when running a java 11 lambda with the latest localstack docker image by docker-compose with the environment variable LAMBDA_JAVA_OPTS=-agentlib:jdwp=transport=dt_socket,server=y,suspend=y,address=_debug_port_
    
It works fine for java8 runtime executions.

Docker command:

> localstack_1  | 2020-01-26T12:42:04:INFO:localstack.services.awslambda.lambda_executors: Running lambda cmd: CONTAINER_ID="$(docker create -i   -e ENV="$ENV" -e DOCKER_LAMBDA_USE_STDIN="$DOCKER_LAMBDA_USE_STDIN" -e HOSTNAME="$HOSTNAME" -e LOCALSTACK_HOSTNAME="$LOCALSTACK_HOSTNAME" -e AWS_LAMBDA_FUNCTION_TIMEOUT="$AWS_LAMBDA_FUNCTION_TIMEOUT" -e AWS_LAMBDA_FUNCTION_NAME="$AWS_LAMBDA_FUNCTION_NAME" -e AWS_LAMBDA_FUNCTION_VERSION="$AWS_LAMBDA_FUNCTION_VERSION" -e AWS_LAMBDA_FUNCTION_INVOKED_ARN="$AWS_LAMBDA_FUNCTION_INVOKED_ARN"  --rm "lambci/lambda:java11" "com.XXX.XXX.Handler")";docker cp "/tmp/localstack/zipfile.0c90736c/." "$CONTAINER_ID:/var/task"; docker start -ai "$CONTAINER_ID";

I think this is due to the fact that the classpath arguments and java opts are only being set if the rutime is equal to LAMBDA_RUNTIME_JAVA8 (line 211 of ocalstack/localstack/services/awslambda/lambda_executors.py , commit 03c6f4bf250edd18eb818ed65090f508636b0bff)
}
    return get_function_version(arn, str(last_version + 1))
def do_list_versions(arn):
    return sorted([get_function_version(arn, version) for version in
                   arn_to_lambda.get(arn).versions.keys()], key=lambda k: str(k.get('Version')))
def do_update_alias(arn, alias, version, description=None):
    new_alias = {
        'AliasArn': arn + ':' + alias,
        'FunctionVersion': version,
        'Name': alias,
        'Description': description or '',
        'RevisionId': str(uuid.uuid4())
    }
    arn_to_lambda.get(arn).aliases[alias] = new_alias
    return new_alias
@cloudwatched('lambda')
def run_lambda(event, context, func_arn, version=None, suppress_output=False, asynchronous=False):
    if suppress_output:
        stdout_ = sys.stdout
        stderr_ = sys.stderr
        stream = StringIO()
        sys.stdout = stream
        sys.stderr = stream
    try:
        func_arn = aws_stack.fix_arn(func_arn)
        func_details = arn_to_lambda.get(func_arn)
        if not func_details:
            return not_found_error(msg='The resource specified in the request does not exist.')
        if not context:
            context = LambdaContext(func_details, version)