"3.7 Volts" is the nominal voltage you get from a single lithium-chemistry cell. It actually ranges from 4.2V fully charged, to around 3.0V flat (any lower than that & you'll be damaging it & shortening its life).
I doubt your circuit is gonna work as you wish. White LEDs have that high forward voltage drop that intrudes on your circuit's balance when battery voltage is low, so your LED current will be all over the place. You really need to be (a) driving each LED with a constant-current circuit, & (b) sensing that force-sensitive resistor with a circuit or microcontroller and then driving the LEDs with a low-side MOSFET accordingly, rather than using the force-resistor in series with the actual LEDs.