For a quick "hack" you need to add LCD4Bit.cpp to the CXXSRC variable in the makefile.
Then in the .pde it must read #include "LCD4Bit.h" (no < >) to reference the lib as a local file. The last step is to put the LCD4Bit.h/.cpp in the same directory as the makefile and the .pde. Then it compiles - at least in my case.
I see, but this is going to a mess after a while. If I change something in the LCD4Bit.cpp, where do I change it? I assume this has to be local, in the directory where the pde is? If you start a new program with the modified library you have to copy the library files to the new program directory.