Stopwatch with Pause/Lap  6 digit 7 seg LED. HELP!

Reading while time is not being updated would probably be good. You said originally something like you wanted to save the lap times and read them out at home.
If you now want to read them out trackside, that is certainly doable.
Reading them while the timer is not running is probably a little cleaner.

Your code is getting kind of long to keep posting here. Can you upload it somewhere where its all in 1 piece for easier vieiwing?

For readback, might be simpler to have another button, like a toggle switch; one side is memory readback, other side is normal operation.

When time is running, after the 10mS update, set the time_update flag to 1 show it is to be updated after the last digit update
if (paused ==0) {time_udpate =1;} // lets the display update

In the memory readout section, udpate the variables to be updated,
and set the same flag
if (time_running == 0 && eeprom_read_complete ==1) {time_update = 1;}

Put a change in your readout code:
{(if time_update == 1){ // doesn't matter who did the update
//do all the shiftouts
time_udpate = 0; // clear for next time
}

So your code will have a few sections:
0. Add a new button, laptime/readback (can be momentary also, with a flag indicating which mode)

  1. If laptime, Read the start/stop button, start time running/stop it.
  2. If laptime, Read the lap button, no display updates with button is pressed, data saved to EEPROM, laptime reset to 0.
  3. If readback, read the memory up button, when pushed read the EEPROM & display. If pushed again, update the address counter, read the next set, & display.

So you're pretty close, just need your logic squared away some.