There are a number of different ways to make files smaller when you export JPGs from Lightroom. You can make the pixel dimensions smaller. You can apply more aggressive JPG compression. And you can strip out redundant metadata using something like ImageOptim.
Another option is to use JPEGmini Pro, an app I've reviewed before. It's a paid app that comes with a companion Lightroom plugin.
JPEGmini's approach is conceptually closest to applying JPG compression. But instead of using the usual JPG algorithm, they've developed their own secret-sauce algorithm that gets vastly better results in the combination of image quality and filesize than you can get from standard JPG compression. After much testing, I decided to built it into my workflow for images on the web, and I've been very impressed. You can read my detailed post on JPEGmini here.
The core JPEGmini app works well. But one of the few extra features you get with the Pro version is the addition of Lightroom and Photoshop plugins. In the case of the Lightroom plugin, it can be inserted into your export process or publish service to run automatically on every image that passes through.
Adding JPEGmini Pro to Lightroom as an Export Plugin
The plugin comes as part of the JPEGmini Pro license. Download it and install it using the usual procedure for installing plugins.
Once it's installed, it becomes an available option for both export operations and publish services. In both cases, you enable it the same way. If you're using it in conjunction with a publish service, you access it through the publish service's settings (when you first create the publish service, or for existing publish services, right click on its name and choose Edit Settings).
Make sure it's enabled in Lightroom's Plugin Manager (File > Plugin Manager).
Now, when you go to export files, you should have the JPEGmini option showing under the Post-Process Actions panel at bottom left.
You'll actually need to expand it--the top level is just a folder name, and the actual plugin is below it. To expand it, just click on the small triangle next to the top JPEGmini. Like this:
Double-click on the plugin. It'll add a new panel towards the end of the export dialog.
As you'll see, there are no options. That's true of the core app version as well. With JPEGmini, it's either on or off--there's no need to mess with settings. So long as you're feeding it JPGs and not some other kind of file, they'll pass through JPEGmini Pro's re-compression, and be smaller in filesize with minimal loss in visual quality.
You can now save the export settings as an export preset, or if you're using a publish service, you can update the publish service's settings.
Using it this way, JPEGmini Pro runs silently. That is, you won't see the usual desktop app panel like the one at the top of this page--the re-compression runs silently in the background.
JPEGmini Pro only works with JPG files. You'll get an error if you try to feed it RAW files or videos.
If you incorporate JPEGmini into a publish service for the web, the JPEGmini compression will only apply to the master file that you pass through it from Lightroom. Many web services and content management systems, like WordPress, create additional resized versions of the image as part of the upload process. Since they're done on the server, they don't pass through JPEGmini Pro. What you can do, if you're so inclined, is periodically download your server's image files and run them all through the JPEGmini app, although I would strongly urge caution before doing that because it's possible to mess up the files and their permissions and cause issues with the images not displaying on your site. That said, it can be done--I do it regularly.
I initially thought it might be possible to automatically run the exported images through the regular JPEGmini by using it as a Post-Processing after export app, but that doesn't work--you'll just get an error message.