AT90CAN128 Random Malfunctions
I know of a coffee-machine which showed the same symptoms, it has a 16x2 character LCD. 1 or 2 wrong symbols, even mixed ones, on each output. Figured it was either a hardware bug or simply too much noise on the I2C signals. (We retired the machine after noticing that the amount of coffee produced per key-press became as inconsistent as the taste.)

I'm guessing your LCD is connected via I2C or SPI, so the next logical step would be to use a logic analyser + voltmeter and check the bus.


Measure SNR
Check if the 'lexical errors' occur prior, during or after transmission 
Check MCU documentation; there should be a way to read the 'reset reason' in firmware to see if it was brownout-reset 
Check voltages; 2.7V as brownout-limit seems very high (most 3V3 MCUs operate at 2.7V) 
Depending whether the bus is I2C or not, maybe it's sinking too much current; make sure the power supply is adequate and the I2C-line-resistors are tuned for your implementation