Three things...

1. Try it. Build the circuit and change the pre-load value for the Timer for 1mS instead of 10mS and change the display to show the additional digit.

2. If it is too slow, try (a) connecting the LCD in 8-bit rather than 4-bit mode to reduce the display time, (b) use a 18F part at 40MHz instead of a 16F part at 4MHz, (c) The danger is you may throw data at the LCD too fast and it won't love you, so try displaying the data only every tenth count, or just at the end with the final result.

3. Consider using the CCP Module of the PIC. You will be able to capture events into the uS range with that. Datasheet of your chosen PIC will explain how to use the CCPM - naturally chose a PIC that has it!