I followed this guide on https://medium.com/@bruce_39084/setting-up-prince-on-aws-lambda-and-api-gateway-4d524dcb035b but I want to just pass in a url instead of a html file. so I made some changes to the index.js and installed axios. I also used the latest prince lambda package as opposed to the 13.5 included in the guide.

var execFile = require('child_process').exec;
const axios = require('axios');

function tinyMultipartParser(data) {
    // assume first line is boundary
    const lines = data.split("\r\n");
    const output = [];
    let in_body = false;
    lines.forEach(line => {
        output.push(line.trim());
    })

    return output.join("\n");

}
exports.handler = async (event, context, done) => {

    if (!event || !event.body) { return done(new Error("No data.")); }
    let body = event.body;
    if (event.isBase64Encoded) {
        body = Buffer.from(body, "base64").toString("ascii");
    }

    const response = await axios.get(body);
    body = response.data;
    const baseUrl = 'https://embed.notMyRealDomain.com'; // Replace with actual base URL

     // Replace relative URLs with absolute URLs
    body = body.replace(/href="([^"]+)"/g, (match, relativeURL) => {
        const absoluteURL = new URL(relativeURL, baseUrl).toString();
        return `href="${absoluteURL}"`;
    });

    body = body.replace(/src="([^"]+)"/g, (match, relativeURL) => {
        const absoluteURL = new URL(relativeURL, baseUrl).toString();
        return `src="${absoluteURL}"`;
    });

    let html = tinyMultipartParser(body);
    let child = execFile("./prince", ["-", "-o", "-"], function (err, stdout, stderr) {
        if (err) { throw new Error(err);}
        if (err === null && (m = stderr.toString().match(/prince:\s+error:\s+([^\n]+)/))) {
            throw new Error(m[1]);
        }
        done(null, {
            "isBase64Encoded": true,
            "statusCode": 200,
            "headers": { "Content-Type": "application/pdf" },
            "body": stdout.toString("base64")
        });
    });
    child.stdin.write(html);
    child.stdin.end();
};

I dumped the "html" variable right before it does exec on prince and both in the html file version and in the pass in a url version the html variable is IDENTICAL but it only works on the html file version and errors in my pass in a url version.