What you propose to do is not impossible

Assumption:
1) you are using one RAM location each for Hours, Minutes and Seconds.
2) You are using 7-segment LED display with the appropriate driver(s) that Erik has mentioned.

I have used a multiplexed display in the past and would recomend the same. One benifit is the reduction in the ic count.

There are two ways to tackle this issue.

1) You store the Hrs, Mins and Seconds in BCD format. This would involve changing the increment routines.
or
2) Have a binary to BCD conversion at the output to display stage.

either ways the hrs/min/seconds data should be available to the display code in bcd format.

given the bcd data you can directly use this (BCD data) as input to the seven segment driver ic's.

The issue gets more complex when you use multiplexing. you multiplex using software and demultiplex on the h/w side by controlling the Cathode/Anode voltage (for CC/CA 7-segments). Actually it is more like a decoder.... Then you need a routine which will control which nibble from which data (hrs/mins/sec) is being displayed at a given time...

In case of the LCD. convert the Higher nibble to ASCII and then the lower nibble to ASCII.and then do whatever you have to to display it!! Have fun...