If i was doing this, i would use a TMR0 register, (okay, i love these) on an interupt been triggered every second, set to incriment some fileregisters, test on overflow from 60, imcremint mins, test again, inc hours, etc.
The main loop of the code itself would constantly be updating the LCD HD44780 is soooooooooooooooo easy. and i left out some "o"s showing my contempt for any one that buys a maxtrix orbital etc. </RANT>
So HD44780 is very forgiving about timing when comunicating with it, so just keep spaming the values in the file register to the LCD (use a lookup table to convert 60d into the correct two byte ASCII codes). The TMR0 overflow interupt would interupt each time on exactly a second.
(using a pre-scaler its easy to get a crystal that will do this for you, better to go for the slower side for better accuracy).