CMake: linking shared library located out of root project - cmake

Question

How to handle library out of project's root?
Currently I want to use CMake to link to my project shared library that is located not in the root directory of a certain library. The library is located in lib, it's shared only between projects located in projects\project_n. Also, I need every project to build the lib independently
.
├── lib
│ ├── CMakeLists.txt
│ ├── src1.c
│ ├── hed1.h
│ ├── src2.c
│ ├── hed2.h
│ ...
│ ├── src_n.c
│ └── hed_n.h
└── projects
├── project_1
│ ├── Src
│ ├── Inc
│ ├── build
│ └── CMakeLists.txt
├── project_2
│ ├── Src
│ ├── Inc
│ ├── build
│ └── CMakeLists.txt
...
└── project_n
├── Src
├── Inc
├── build
└── CMakeLists.txt
Currently my lib\CMakeLists.txt looks like that:
cmake_minimum_required(VERSION 3.20)
file(GLOB_RECURSE SRCS *.c)
add_library(lib SRCS)
Part of code in projects\project_1\CMakeLists.txt responsible for lib linking looks like that:
add_subdirectory(../../lib build)
target_include_directories(${PROJECT_NAME} PUBLIC ../../lib)
target_link_directories(${PROJECT_NAME} PRIVATE ../../lib)
target_link_libraries(${PROJECT_NAME} lib)
Currently I'm getting Errors belows:
CMake Error at CMakeLists.txt:65 (target_include_directories):
Cannot specify include directories for target "project_1" which is
not built by this project.
CMake Error at CMakeLists.txt:66 (target_link_directories):
Cannot specify link directories for target "project_1" which is not
built by this project.
CMake Error at CMakeLists.txt:67 (target_link_libraries):
Cannot specify link libraries for target "project_1" which is not
built by this project.