Having a look at the AWS documentation,
https://docs.aws.amazon.com/cognito/latest/developerguide/cognito-user-identity-pools-working-with-aws-lambda-triggers.html#cogni
Yes, there's absolutely a way! You need to use AWS javascript SDK in your Lambda handler:
const AWS = require('aws-sdk');
AWS.config.update({region: 'ap-southeast-1'});
const cognitoidentityserviceprovider =
new AWS.CognitoIdentityServiceProvider({
apiVersion: '2016-04-18'
});
cognitoidentityserviceprovider.adminUpdateUserAttributes(
{
UserAttributes: [
{
Name: 'YOUR_USER_ATTRIBUTE_NAME',
Value: 'YOUR_USER_ATTRIBUTE_VALUE'
}
],
UserPoolId: event.userPoolId,
Username: event.userName
},
function(err, data) {
...
}
);
Make sure to give your Lambda function the right policies (i.e. allows "cognito-idp:AdminUpdateUserAttributes" action) and the user pool has the attribute defined.