I2C level converter stops bus
These converters have a definite high voltage (HV) and low voltage (LV) side. Make sure to interconnect the 5V LCD to the HV side of the level translator. The 3.3V interface of the Arduino will connect to the LV side of the level translator. 

You need to make sure to connect GND of the Arduino, LCD and the level translator all together. The 5V supply rail that powers the LCD also needs to connect to the HV VDD connection of the level converter. Likewise the 3.3V rail from the Ardino needs to connect to the LV VDD connection of the level converter.

If you mistakenly swap the HV and LV sides of the converter the I2C bus will fail to operate properly because of the improper bias for the body diodes of the FETs on the level translator.

Also as mentioned in other comments you need to ensure that the SCL and SDA lines on both sides of the level translator have their own sets of pullup resistors. It is doubtful that the level translator has pullups built in since the value of pullup resistors for I2C can be very system specific. 

Finally if you could share a link to the schematic of the level translator it may be possible to offer you further guidance.