You can include LCD4Bit to your own library, add a member of LCD4Bit to the library class, create an instance of it in the libraries constructor and if you really need a pointer to this LCD4Bit instance you can add a getter method to your library, that returns this pointer.
(Library != application)
— MyLib.h —
lcd.init(); // check LCD4Bit library to see how to init this instance correctly
//do some of your library stuff here
If you want to use the LCD4Bit in your application, you need to include LCD4Bit.h, initialize your library “MyLib”, before you do something with the LCD.
— MyProject.pde —
LCD4Bit* pLCD = 0;
pLCD = myLib.getLCDPointer();
If you want to do the “main stuff” within your library and use the LCD within your application additionally, may be just for textout, then you should add a textOut(…) to your library instead of access the lcd via a pointer from the application. This can avoid mixed output, because you can control within your library, if the application is allowed to textout something at this moment. Otherwise your lib draws the menu and the application could write some other text at the same time.
I had no time to test this, but it should work LIKE this.