LCD library and timer2 CTC interrupt not working together
You're getting interrupt every 16th CPU clock cycle. The ISR handler might be even longer than that and your code and lower priority ISRs suffers by "starvation" as MCU can't do anything else than processing ISR.

If you use prescaler value 8, then you have 1/2us resolution of TCNT2 and overflow interrupt (in normal mode) occurs every 128us, so there will be enough time to do something else. However, if you want atomic value of TCNT2 and counted value from ISR handler, you'll have to stop Timer2 for a while.