I'm using Arduino UNO R3 and it's pins D2&3 to communicate with LM339 (connected to car ECU) via softserial. Everything works with no LCD SHIELD (showed at serial port monitor), when I add LCD SHIELD... communication just stops.
I don't see a reason to supply more info - I told what I'm using, where and how.
Anyway, I tried without shield but with standard LCD (16x2), result was the same - LCD works but no communication, when I disconnect the LCD - communication works.
Technically there is no reason that this would happen - there is no pin conflict, and as far as Arduino documentation goes, there is no communication conflict. But the problem exists.
So... I'v used I2C LCD, and... now all just works fine. There was no change in program/wiring (except LCD of course). Problem solved.
So to anyone having problem with standard LCD and interrupts at D2&3 - use I2C LCD instead.
Off the top of my head I can think of few things that could create these symptoms. But given you won't supply enough information to those that may offer to help you and you seem to have no interest in tracking down the root cause, I guess we will never know.
While that may have "worked" in this specific situation, normally moving from direct pin i/o control to using the Wire library through an i2c port expander to control an LCD adds overhead and latency that can be detrimental to certain situations.
But again, since we have no idea of your exact setup including any visibly of your sketch code we can not make anything from this information.