I have several libraries made by myself (a geometry library, a linked list library, etc). I want to make a header file to include them all in one lib.h. Could I do something like this:
Yes, this will work.
Note, however, that if you include a lot of headers in this file and don't need all of them in each of your source files, it will likely increase your compilation time.
It also makes it more difficult to figure out on which header files a particular source file actually depends, which may make code comprehension and debugging more difficult.