When using ON INTERRUPT, the GIE bit is controlled by PBP.
Any attempts to change it manually will cause problems.

And the IOC port change interrupt, doesn't save the state of the PINs for you. If you're just getting a quick pulse, it's possible that the pulse is gone by the time you try to display the pins, or determine who shot you with what.

The very first statement in the interrupt handler should read PORTA and save the value in a variable. Then use that variable throughout your handler, instead of the pins themselves.

The IOC interrupt also triggers on any pins transition from low to high, or high to low.
But your program is only looking for HIGH states. If it makes it all the way through the handler before the pulse goes away, then you will get another interrupt at the end of the input pulse. This time it'll look like all the pins are at their default state, as if nothing changed. You'll need to account for the second interrupt, somehow.

You're also clearing the interrupt flag in 2 places in the handler, one at the beginning, and another at the end of the handler. The first one attempts to clear the flag, before PORTA has been read. But it won't clear the flag, because the mismatch condition still exists.
Read PORTA first, then clear the flag.

At the end of the handler, it clears the flag, but doesn't read PORTA.
With things like LCDOUT's in the handler, it can take quite a while to complete the handler, and the PINs may have changed in the mean time, so it would be necessary to read PORTA again before clearing the flag.

hth,