Some webhosts won't let you run composer. Others don't give you command-line access at all. In these circumstances, you'll need to commit your dependencies to your VCS. To be clear, neither I nor the Composer docs recommend this. But if you must, these tips might help.
1. Remove everything from your .gitignore
The .gitignore file that ships with Lightning Project intentionally ignores the folders that Composer uses for dependencies. You'll need to remove everything from that file with the exception of /docroot/sites/default/files line.