According to the datasheet, the backlight LED on the LCD screen (just LCD screen, no I2C module) is connected to pins 15 and 16:
https://cdn-shop.adafruit.com/datasheets/TC1602A-01T.pdf, so the backlight LED can be either on or off.
Our LCD screen has the I2C module soldered on the back: it is possible to turn the LED on and off in software (see
http://stackoverflow.com/questions/28385369/python-code-for-a-16x2-lcd-via-i2c-gives-alternate-results). However, we don't have this feature implemented in our code yet, I was planning to do that for quite some time though.
So short answer is: no, it is not possible to dimm the LCD in software on your LiV. However, you can hack your unit and wire a potentiometer in series with your backlight LED (or use a transistor) to control the light intensity. Another option would be to use PWM to control the light intensity of your LED, something like:
http://forum.arduino.cc/index.php?topic=153916.0 - this is an Arduino project but the idea of PWM control is pretty general. Second option would allow you to control backlight in software.