it all depends on what you mean by simulation.
most of the toolchains out there can be used to step through the execution, and allow you to watch the registers / variables / GPIO, etc.
very few of them will actually allow you to hook up a LCD (graphics or character) to the MCU, run your program on the MCU and see how the LCD reacts to it.
the most used "simulator" that includes both mcus and lcd displays is Proteus by LabCenter. it is a mixed signal simulator, and has a few MCU families (pic, 8051, arm, for example), and some lcd models, and of course transistors, led, etc.
multisim (available from NI) does some of that as well, on a very limited basis.