Similarly to how Composer loads packages into the vendor directory, this directory will contain WooPayments-specific libraries. There are a couple of differences here:

All packages have their namespaces prefixed by WooPayments\Vendor\ to prevent conflicts with other plugins. This is automated through the coenjacobs/mozart package.
Even though vendor packages are not commited to git, the packages within lib/packages will be commited.

Currently the directory only contains the League\Container package.

Do not make any changes within packages, they will be lost!

Adding new packages

Please be mindful of adding packages to lib, as they will both live in git, require maintenance, and be distributed within the plugin.

Navigate to this directory lib.
Modify extra.mozart.packages within composer.json, adding the new package.
Require the package through Composer (ex. composer require --dev provider/package).
Open a PR, and commit the result.

Updating packages

Navigate to this directory lib.
Run composer update.
Open a PR, and commit the result.