index.js

module.exports.handler = async (event) => {
    console.log(JSON.stringify(event, 2));
    return "Echoing your message: " + event.echo;
};

template.yaml

AWSTemplateFormatVersion: '2010-09-09'
Transform: AWS::Serverless-2016-10-31
Resources:

  MyLambdaRouteHandlerFunction:
    Type: AWS::Serverless::Function
    Properties:
      Handler: index.handler
      Timeout: 30
      Runtime: nodejs10.x
      CodeUri: ./
      Policies:
        - AWSLambdaFullAccess
        - CloudWatchLogsFullAccess

  MyWebSocketApi:
    Type: AWS::ApiGatewayV2::Api
    Properties:
      Name: MyWebSocketApiRouteResponse
      ProtocolType: WEBSOCKET
      RouteSelectionExpression: "$request.body.action"

  TestRoute:
    Type: AWS::ApiGatewayV2::Route
    Properties:
      ApiId: !Ref MyWebSocketApi
      RouteKey: test
      RouteResponseSelectionExpression: $default
      AuthorizationType: NONE
      Target: !Join
        - '/'
        - - 'integrations'
          - !Ref TestLambdaIntegration

  TestLambdaIntegrationResponse:
    Type: AWS::ApiGatewayV2::IntegrationResponse
    Properties: 
      ApiId: !Ref MyWebSocketApi
      IntegrationId: !Ref TestLambdaIntegration
      IntegrationResponseKey: $default

  TestLambdaIntegration:
    Type: AWS::ApiGatewayV2::Integration
    Properties:
      ApiId: !Ref MyWebSocketApi
      Description: Test Integration
      IntegrationType: AWS
      IntegrationUri: 
        Fn::Sub:
            arn:aws:apigateway:${AWS::Region}:lambda:path/2015-03-31/functions/${MyLambdaRouteHandlerFunction.Arn}/invocations

  MyRouteResponse:
    Type: AWS::ApiGatewayV2::RouteResponse
    Properties:
      RouteId: !Ref TestRoute
      ApiId: !Ref MyWebSocketApi
      RouteResponseKey: $default

  Deployment:
    Type: AWS::ApiGatewayV2::Deployment
    DependsOn:
      - TestRoute
    Properties:
      ApiId: !Ref MyWebSocketApi

  Stage:
    Type: AWS::ApiGatewayV2::Stage
    Properties:
      StageName: v1
      Description: Version 1 'stage'
      DeploymentId: !Ref Deployment
      ApiId: !Ref MyWebSocketApi

  ApiGatewayLambdaInvokePermission:
    Type: AWS::Lambda::Permission
    DependsOn:
      - MyWebSocketApi
      - MyLambdaRouteHandlerFunction
    Properties:
      Action: lambda:InvokeFunction
      FunctionName: !Ref MyLambdaRouteHandlerFunction
      Principal: apigateway.amazonaws.com

Outputs:
    MyWebSocketApi:
      Description: "API Gateway endpoint URL for Prod stage for Hello World function"
      Value: !Sub "https://${MyWebSocketApi}.execute-api.${AWS::Region}.amazonaws.com/v1"