Problem with connecting an LCD 16x2

Yes correct the diode won't limit the current directly however it will do the thing, since 4.2v and 0.7v add up to 4.9 volts. I use it myself, the LED backlight has a resistor but that is not enough, very bright, adding a diode, brightness dropped down to moderate levels. It's not always handy to have so many resistors around.

The problem is that you just don't understand the theory. The voltage drop across a diode is a dependent variable. It depends on a specific amount of current flowing through the diode which must be determined by some external component, typically a resistor.

The LEDs in the backlight will only exhibit a voltage drop of 4.2 Volts when their nominal current flows through them. The series diode will only exhibit a voltage drop of 0.7 Volts (assuming it is a typical silicon power diode) when its nominal current flows through it. The diodes themselves cannot be used to control or determine this current.

Don