The Arduino Uno is power by 12V batteries. I'm getting 5.02V on the Arduino when the project is running. When I lit the LCD, the voltage is still 5.02V. ...
The voltage on the TMP36 is 5.02V without the LCD lit. When lit, it drops to between 4.70 and 4.74V. That is my problem, and I don't know how to solve it.
The question is how does that happen if your Arduino +5 regulated voltage stays constant?
It happens because the wires and the connections between the wires and the breadboard are not ideal, they have resistance. If the backlight does not have a current limiting resistor, and if it should have one, then the excessive current is causing a voltage drop in the non ideal wiring between the Arduino and the breadboard.
Post a link to the LCD datasheet and perhaps we can tell if a resistor is required and what size it should be.
Don