I had this issue, which originated from an invalid handler code which looks completely fine:
exports.handler = (event, context) => {
    return {
       isBase64Encoded: false,
       body: JSON.stringify({ foo: "bar" }),
       headers: {
          'Access-Control-Allow-Origin': '*',
       },
       statusCode: 200,
    };
}
This handler was previously declared async without ever using await, so I removed the async keyword without realizing that Lambda expects either using async/await/Promise or callback return method.
I got the hint from examining the somewhat confusing API Gateway response logs:
> Endpoint response body before transformations: null
The way to fix it would be to either
- Add the asynckeyword (async function implicitly returns a Promise):
exports.handler = async (event, context) => {
    return {
        isBase64Encoded: false,
        body: JSON.stringify({ foo: "bar" }),
        headers: {
            'Access-Control-Allow-Origin': '*',
        },
        statusCode: 200,
    };
}
exports.handler = (event, context) => {
    return new Promise((resolve) => resolve({
        isBase64Encoded: false,
        body: JSON.stringify({ foo: "bar" }),
        headers: {
            'Access-Control-Allow-Origin': '*',
        },
        statusCode: 200,
    }));
}
exports.handler = (event, context, callback) => {
    callback({
        isBase64Encoded: false,
        body: JSON.stringify({ foo: "bar" }),
        headers: {
            'Access-Control-Allow-Origin': '*',
        },
        statusCode: 200,
    });
}