Lambda expects an API and you are not following it. As in this documentation, Lambda expects:
exports.myHandler = function(event, context, callback) {};
Then it would call this:
const handlers = require('your-module');
handlers();
The ES6 classes have to create with new. That is the issue. As the Lambda function is expecting a function, the function should be callable and not constructible. For example. Check this:
class widget {
constructor(event, context, callback) {
callback(null, `all seems well!`);
}
}
exports.myHandler = function(event, context, callback) {
new widget(event, context, callback);
};