Bad news, good news, better news, amd best news:
The Bad News: Browsers only render HTML, with some visual attributes defined in CSS and interactivity provided through the only language browsers natively understand, JavaScript. LiveCode stack files are among the many formats browsers simply aren't designed to handle, so there's no way to display a LiveCode stack file in a browser.
The Good News: HTML, CSS, and JavaScrtipt are just plain text, and LiveCode is unusually adept at manipulating text. Many of us produce Web sites using LiveCode as a key part of the process, generating HTML/CSS to translate layouts to a Web-ready form, and even assembling JavaScript snippets to deliver the interactivity for those pages.
The Better News: While Web browsers can't render LiveCode stacks, many of the benefits of delivering stacks over the Web can be achieved very easily by building a standalone that is in effect a custom browser, one that downloads and runs LiveCode stacks from servers similarly to how traditional browsers download and render HTML files. There's an example of this in the IDE (thought woefully in need of a content update, coming as soon as I finish some client work): see Development->Plugins->GoRevNet. Once you select that plugin, it downloads and runs a stack that lives on one of my servers. This is super-easy to do, and you can even store the files compressed on the server and decompress them in the standalone for faster transfer times using LiveCode's built-in compress and decompress functions. This won't satisfy needs for running in a Web browser specifically, but can provide many of the same benefits in terms of instant delivery of the latest versions of your stacks, providing ultra-simply deployment with a UI dedicated to the task your app supports. Right now a majority of the projects I'm working on are standalones that use downloaded stack files used in intranet and extranet contexts.
The Best News: For projects that require deployment through a traditional Web browser, RunRev just successfully completed a crowd-funding campaign to deliver a turnkey solution to translate LiveCode into HTML/CSS/JavaScript automatically. It's a rather huge effort that's estimated to take about a year to deliver, but once completed promises the simplest means of delivering LiveCode-based projects to traditional Web browsers - see this page for details:
http://livecode.com/livecode-to-html5/