You need to call your handler function from another file lets say testHandler.js in order to run via NodeJs.

This will be done like this

//import your handler file or main file of Lambda
let handler = require('./handler');

//Call your exports function with required params
//In AWS lambda these are event, content, and callback
//event and content are JSON object and callback is a function
//In my example i'm using empty JSON
handler.handlerEvent( {}, //event
    {}, //content
    function(data,ss) {  //callback function with two arguments 
        console.log(data);
    });

Now you can use node testHandler.js to test your handler function.

EDIT: Sample Event and content data as requested

Event:

{
    "resource": "/API/PATH",
    "path": "/API/PATH",
    "httpMethod": "POST",
    "headers": {
        "Accept": "*/*",
        "Accept-Encoding": "gzip, deflate, br",
        "Accept-Language": "en-GB,en-US;q=0.9,en;q=0.8",
        "cache-control": "no-cache",
        "CloudFront-Forwarded-Proto": "https",
        "CloudFront-Is-Desktop-Viewer": "true",
        "CloudFront-Is-Mobile-Viewer": "false",
        "CloudFront-Is-SmartTV-Viewer": "false",
        "CloudFront-Is-Tablet-Viewer": "false",
        "CloudFront-Viewer-Country": "IN",
        "content-type": "application/json",
        "Host": "url.us-east-1.amazonaws.com",
        "origin": "chrome-extension://fhbjgbiflinjbdggehcddcbncdddomop",
        "User-Agent": "Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/68.0.3440.106 Safari/537.36",
        "Via": "2.0 XXXXXXXXXXXXXX.cloudfront.net (CloudFront)",
        "X-Amz-Cf-Id": "XXXXXXXXXX51YYoOl75RKjAWEhCyna-fuQqEBjSL96TMkFX4H0xaZQ==",
        "X-Amzn-Trace-Id": "Root=1-XXX03c23-25XXXXXX948c8fba065caab5",
        "x-api-key": "SECUREKEY",
        "X-Forwarded-For": "XX.XX.XXX.XXX, XX.XXX.XX.XXX",
        "X-Forwarded-Port": "443",
        "X-Forwarded-Proto": "https"
    },
    "multiValueHeaders": {
        "Accept": [ "*/*" ],
        "Accept-Encoding": [ "gzip, deflate, br" ],
        "Accept-Language": [ "en-GB,en-US;q=0.9,en;q=0.8" ],
        "cache-control": [ "no-cache" ],
        "CloudFront-Forwarded-Proto": [ "https" ],
        "CloudFront-Is-Desktop-Viewer": [ "true" ],
        "CloudFront-Is-Mobile-Viewer": [ "false" ],
        "CloudFront-Is-SmartTV-Viewer": [ "false" ],
        "CloudFront-Is-Tablet-Viewer": [ "false" ],
        "CloudFront-Viewer-Country": [ "IN" ],
        "content-type": [ "application/json" ],
        "Host": [ "apiurl.us-east-1.amazonaws.com" ],
        "origin": [ "chrome-extension://fhbjgbiflinjbdggehcddcbncdddomop" ],
        "User-Agent": [ "Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/68.0.3440.106 Safari/537.36" ],
        "Via": [ "2.0 XXXXXXXXXXXXXX.cloudfront.net (CloudFront)" ],
        "X-Amz-Cf-Id": [ "XXXXXXXXXhCyna-fuQqEBjSL96TMkFX4H0xaZQ==" ],
        "X-Amzn-Trace-Id": [ "Root=1-XXXXXXX67339948c8fba065caab5" ],
        "x-api-key": [ "SECUREAPIKEYPROVIDEDBYAWS" ],
        "X-Forwarded-For": [ "xx.xx.xx.xxx, xx.xxx.xx.xxx" ],
        "X-Forwarded-Port": [ "443" ],
        "X-Forwarded-Proto": [ "https" ]
    },
    "queryStringParameters": null,
    "multiValueQueryStringParameters": null,
    "pathParameters": null,
    "stageVariables": null,
    "requestContext": {
        "resourceId": "xxxxx",
        "resourcePath": "/api/endpoint",
        "httpMethod": "POST",
        "extendedRequestId": "xxXXxxXXw=",
        "requestTime": "29/Nov/2018:19:21:07 +0000",
        "path": "/env/api/endpoint",
        "accountId": "XXXXXX",
        "protocol": "HTTP/1.1",
        "stage": "env",
        "domainPrefix": "xxxxx",
        "requestTimeEpoch": 1543519267874,
        "requestId": "xxxxxxx-XXXX-xxxx-86a8-xxxxxa",
        "identity": {
            "cognitoIdentityPoolId": null,
            "cognitoIdentityId": null,
            "apiKey": "SECUREAPIKEYPROVIDEDBYAWS",
            "cognitoAuthenticationType": null,
            "userArn": null,
            "apiKeyId": "xxXXXXxxxxxx",
            "userAgent": "Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/68.0.3440.106 Safari/537.36",
            "accountId": null,
            "caller": null,
            "sourceIp": "xx.xxx.xxx.xxx",
            "accessKey": null,
            "cognitoAuthenticationProvider": null,
            "user": null
        },
        "domainName": "url.us-east-1.amazonaws.com",
        "apiId": "xxxxx"
    },
    "body": "{\n    \"city\": \"Test 1 City\",\n    \"state\": \"NY\",\n    \"zipCode\": \"11549\"\n}",
    "isBase64Encoded": false
}

Content:

{
    "callbackWaitsForEmptyEventLoop": true,
    "logGroupName": "/aws/lambda/lambda-name",
    "logStreamName": "2018/11/29/[$LATEST]xxxxxxxxxxxb",
    "functionName": "lambda-name",
    "memoryLimitInMB": "1024",
    "functionVersion": "$LATEST",
    "invokeid": "xxxxx-xxx-11e8-xxx-xxxxxxxf9",
    "awsRequestId": "xxxxxx-xxxxx-11e8-xxxx-xxxxxxxxx",
    "invokedFunctionArn": "arn:aws:lambda:us-east-1:xxxxxxxx:function:lambda-name"
}

I have used like this.

//index.js

const user = require('./user').user;
const handler = function (event, context, callback) {
  user.login(username, password)
    .then((success) => {
      //success
    })
    .catch(() => {
      //error
    });
};

exports.handler = handler;



//user.js
const user = {
  login(username, password) {
   return new BPromise((resolve, reject) => {
     //do what you want.
   });
  }
};
export {user};