How to clone a specific subdirectory as root in Git?

Question

I have a library Git repo:

Library Root
 ┗ sample
 ┗ lib
 ┗ README.md

I want to clone only lib directory at the repo to my project like below:

Project Root
 ┗ app
 ┗ lib // Cloned from the library repo
 ┗ some files

I know about the sparse checkout, but it retains the root directory. For example,

Project Root
 ┗ app
 ┗ Library Root
    ┗ lib
 ┗ some files

The lib at the Library Repo and Project must be able to sync each other

Is there any way to achieve this? Thank you in advance. :)