I want to write a (.c lib) for Lite_C and C ,and they can both use this lib.
Is it able to do?

Pretty straightforward, fire up your favourite IDE and create a new DLL with it.
To link the DLL at runtime in your Lite-C project, use LoadLibrary() and to resolve a symbol use GetProcAddress(). To link it with your normal C project... well, depends on your IDE and linker, but usually they should take care of it.

That's for dynamically loading the dll.

To statically do that, for lite-c part, if it's a C dll you only need the header and say that the functions on that header is in your dll.
There was a macro sort of like API(function_name,dll_filename), you should search that too.

http://www.conitec.net/beta/litec_api.htm