No, that is not how Lightroom works. Lightroom is a single-user application. It opens a catalog which is a database. That catalog keeps track of the images that have been imported and are on the computer where they were imported. Those images are not "in" Lightroom. They are in the folders where you chose to import them. The catalog only keeps track of where the images are located, as well as any adjustments that you have made to them and any keywords and star ratings and color labels that you have assigned to those images. The images themselves remain unchanged. If you want those same images and all of the adjustments available on another computer you need to take a copy of the catalog as well as all of the master images to the other computer. You would be wise to take the images in exactly the same folder structure as they are in on the original computer. You would also be wise to have those images arranged within a single master folder. You can have as many folders within that master folder as you wish. But it would be well to have everything within a master image folder.
If you have Lightroom CC then you have access to Lightroom Mobile and Lightroom on the web. This enables you to create collections that can be shared on the web and on your mobile devices. This will enable you to use the Lightroom mobile app to view and edit images on your android and IOS mobile devices as well as access those shared images by going to Lightroom.adobe.com from any computer. The editing tools are a little different and don't give you quite as much flexibility as the full Lightroom program on your computer does, but at least you can work on your images when you are away from home. Here are links to some training videos that might help you understand how to use Lightroom. You didn't indicate what version of Lightroom you have. Some of the training videos refer to Lightroom CC. Most of the information will apply to any version of Lightroom.