a few more details on the parts used, 

The parts used, where mainly chosen by the immediate availability in my box of bits.
and may NOT be the best parts for the job. 

Lithium-Ion,  power management
I used an TP4056 based  micro USB -> Lithium-ion battery charger board,
to charge the lithium-polymer battery,
it includes  Under voltage cut-off to protect from undercharging the battery
(i don't believe its ideal for lithium-polymer batteries, but does the job)

Raspberry pi zero power / USB 5V
the raspberry pi needs 5V for power, as well as for the USB ports, 
I used a MT3608 based boost converter module to step this up from the battery voltage
while they appear to be "rated" for 2A  I'm probably driving it a bit hard.  

LCD adapter and back-light. 
I did not buy a module to interface with the LCD,  I repurposed an old board i had with the 40pin LCD connector, I did point to point wiring to the raspberry pi GPIO header
combined this with a SX1308 based boost converter module to step the battery voltage up to 23v for the LED back-light

I would consider getting a dedicated LCD interface module. possibly with the back-light step up,  
there are a few out there  
(having the boost convert separate, may make it easier to make it fit somewhere.)