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)
result.update(format_func_details(func_details))
    if isinstance(result, Response):
        return result
    return jsonify(result or {})
@app.route('%s/functions/<function>/code' % PATH_ROOT, methods=['GET'])
def get_function_code(function):
    """ Get the code of an existing function
        ---
        operationId: 'getFunctionCode'
        parameters:
    """
    arn = func_arn(function)
    lambda_cwd = arn_to_lambda[arn].cwd
    tmp_file = '%s/%s' % (lambda_cwd, LAMBDA_ZIP_FILE_NAME)
    return Response(load_file(tmp_file, mode='rb'),
            mimetype='application/zip',
            headers={'Content-Disposition': 'attachment; filename=lambda_archive.zip'})
@app.route('%s/functions/<function>/configuration' % PATH_ROOT, methods=['GET'])
def get_function_configuration(function):
    """ Get the configuration of an existing function
        ---
        operationId: 'getFunctionConfiguration'
        parameters:
    """
    arn = func_arn(function)
    lambda_details = arn_to_lambda.get(arn)
    if not lambda_details:
        return not_found_error(arn)
    result = format_func_details(lambda_details)
    return jsonify(result)