How to use a logic level shifter for 1602 LCD
I am not an electronics engineer... that being said, I have used a 1602 LCD screen with my Orange PI Zero, which, like your ESP, also outputs SDA and SCL at 3.3V (and not the 5V expected by the 1602). Just like in your setup, the screen appears to work perfectly - that is, provided it is fed with 5V at its VCC pin. EDIT: But keep reading - in the end, it turned out that it wasn't "working perfectly"...

To be 100% sure, you'd use your level shifter as follows:


Connect the two GNDs of the shifter to any of your ESP's GND pins
Connect 3.3V from the ESP to the "LV" of the shifter
Connect 5V to the "HV" of the shifter.
Connect the SDA and SCL pins of your ESP to two "LV"s of the shifter (e.g. LV1 and LV2)
Connect the corresponding HV pins to the SDA and SCL of the screen (e.g. HV1 and HV2).


That should work - and give you peace of mind that the screen is not slowly frying the electronics of your ESP.

I should probably follow my own advice and do the same for my very similar Orange PI Zero setup :-)

EDIT: Updated, a week later: 



I bought a 4-channel level shifter from ebay (I don't post the link for fear of being classified as a spammer). Very cheap - 1.5 Euros - and 1 Euro for shipping to the NL (which took two days to arrive from France). In fact, I bought two of the shifters - having a spare is always good policy :-) 

I soldered the headers and connected the shifter as I described above; and everything worked fabulously. Curious to see what was the actual impact, I also used my scope to see the level of SDA and SCL before and after the use of the shifter. It turned out that when I was connecting the Orange PI Zero's SDA/SCL directly to the screen's SDA/SCL, the level was pulled up to 3.9V - that is, above the 3.3V that the GPIO pins should be... 

It wasn't 5V - but then again, it wasn't 3.3V either. I am guessing the I2C circuit that is attached to the 1602 causes some voltage drop of its own - taking it down to 3.9V. But the important thing is that the end result was 3.9V on the SDA and SCL pins of the Orange PI Zero - above 3.3V... Instead, with the shifter in place as described above, the values are now exactly right: both SDA and SCL are at 3.3V.

I do feel safer about my PI now :-)