Invoke AWS Lambda with Amazon SNS from Different Accounts?

Here you go, below link has all you need

https://docs.aws.amazon.com/lambda/latest/dg/with-sns-create-x-account-permissions.html

Steps mentioned in above link:

1) From account A, create the Amazon SNS topic:

aws sns create-topic --name lambda-x-account

Note the topic arn that is returned by the command. You will need it when you add permissions to the Lambda function to subscribe to the topic.

2) From account B, create the Lambda function. For the runtime parameter, select either nodejs6.10, nodejs4.3, python3.6, python2.7 or java8, depending on the code sample you selected when you created your deployment package.

aws lambda create-function \
    --function-name SNS-X-Account \
    --runtime runtime language \
    --role role arn \
    --handler handler-name \
    --description "SNS X Account Test Function" \
    --timeout 60 \
    --memory-size 128 \
    --zip-file fileb://path/LambdaWithSNS.zip  

Note the function arn that is returned by the command. You will need it when you add permissions to allow Amazon SNS to invoke your function.

3) From account A add permission to account B to subscribe to the topic:

aws sns add-permission \
    --region us-east-1 \
    --topic-arn Amazon SNS topic arn \
    --label lambda-access \
    --aws-account-id B \
    --action-name Subscribe ListSubscriptionsByTopic Receive

4) From account B add the Lambda permission to allow invocation from Amazon SNS:

aws lambda add-permission \
    --function-name SNS-X-Account \
    --statement-id sns-x-account \
    --action "lambda:InvokeFunction" \
    --principal sns.amazonaws.com \
    --source-arn Amazon SNS topic arn 

In response, Lambda returns the following JSON code. The Statement value is a JSON string version of the statement added to the Lambda function policy:

{
    "Statement": "{\"Condition\":{\"ArnLike\":{\"AWS:SourceArn\":\"arn:aws:lambda:us-east-1:B:function:SNS-X-Account\"}},\"Action\":[\"lambda:InvokeFunction\"],\"Resource\":\"arn:aws:lambda:us-east-1:A:function:SNS-X-Account\",\"Effect\":\"Allow\",\"Principal\":{\"Service\":\"sns.amazonaws.com\"},\"Sid\":\"sns-x-account1\"}"
}    

Note

Do not use the --source-account parameter to add a source account to the Lambda policy when adding the policy. Source account is not supported for Amazon SNS event sources and will result in access being denied. This has no security impact as the source account is included in the source ARN.

5) From account B subscribe the Lambda function to the topic:

aws sns subscribe \
    --topic-arn Amazon SNS topic arn \
    --protocol lambda \
    --notification-endpoint arn:aws:lambda:us-east-1:B:function:SNS-X-Account

You should see JSON output similar to the following:

{
    "SubscriptionArn": "arn:aws:sns:us-east-1:A:lambda-x-account:5d906xxxx-7c8x-45dx-a9dx-0484e31c98xx"
}

6) From account A you can now test the subscription. Type "Hello World" into a text file and save it as message.txt. Then run the following command:

aws sns publish \
    --topic-arn arn:aws:sns:us-east-1:A:lambda-x-account \
    --message file://message.txt \
    --subject Test

This will return a message id with a unique identifier, indicating the message has been accepted by the Amazon SNS service. Amazon SNS will then attempt to deliver it to the topic's subscribers.

Note

Alternatively, you could supply a JSON string directly to the message parameter, but using a text file allows for line breaks in the message.