Use resource created in other stack

Question

I have created a lambda function in one stack and now want to use it in my ApiGateway stack as lambda handler.

How can I pass a resource from one stack to another? I have only found either TypeScript examples or bad python examples that were either not working or missing the important step.

main

#!/usr/bin/env python3

import aws_cdk as cdk

from cdk.api_stack import ApiStack
from cdk.lambda_stack import LambdaStack


app = cdk.App()
LambdaStack(app, "lambda")
ApiStack(app, "api", gitlabUtilsLambda=LambdaStack.outputLambda)


app.synth()

Lambda Stack

from constructs import Construct
from aws_cdk import (
    Stack,
    aws_lambda as _lambda,
)

class LambdaStack(Stack):

    def __init__(self, scope: Construct, construct_id: str, **kwargs) -> None:
        super().__init__(scope, construct_id, **kwargs)

        gitlabUtilsLambda = _lambda.Function(
            self, "handler",
            runtime=_lambda.Runtime.PYTHON_3_9,
            code=_lambda.Code.from_asset('lambda'),
            handler='createGroup.handler',
        )

        self.outputLambda = gitlabUtilsLambda

The ApiGateway stack where i want to use the lambda function:

from constructs import Construct
from aws_cdk import (
    Stack,
    aws_apigateway as apigw,
)


class ApiStack(Stack):

    def __init__(self, scope: Construct, construct_id: str, **kwargs) -> None:
        super().__init__(scope, construct_id, **kwargs)

        api = apigw.LambdaRestApi(
            self, 'gitlab',
            handler=kwargs.get("gitlabUtilsLambda"),
            default_method_options=apigw.MethodOptions(api_key_required=True)
        )

        plan = api.add_usage_plan(
            id="UsagePlan")

        plan.add_api_stage(stage=api.deployment_stage)

        apiKey = api.add_api_key(
            id="MyKey", value="xxx")
        plan.add_api_key(apiKey)

Here I´m currently trying it to use with handler=kwargs.get("gitlabUtilsLambda"), but this results in an error.