MIKROE-55 - LCD Datasheet
If you (both!)


have a 3.5V supply that is sufficently accurate
can live with a LED current that can be any value between 13 mand 20 mA


then you can ideed apply 3.5V directly.

For a higher voltage you must add an external resistor. For instance, for 5V you need a regsistor of 1.5V/16mA `= 100 Ohm.