Understanding "Current Draw" in terms of "Ohm's Law"
You have a number of misunderstandings.

Ohm's law applies to resistors.  LEDs are non-linear elements and therefore Ohm's law doesn't apply.

Elements in series have the same current flowing through them.  If you have 3 LEDs in series and one has 50mA flowing in it, so do the other two.  Total current? 
50mA.  Your source has to have enough voltage to "overcome" the sum of the forward voltages of the LEDs plus some headroom for whatever is regulating or limiting the current.

Elements in parallel have the same voltage across them, and may have different currents flowing through them.  The sum of the currents through each element is the total current drawn by the elements from the source.  Three parallel LEDs with 50mA flowing in each would draw 150mA from the supply.

You have to control the current through LEDs by using a constant current drive or a resistor in series to set the appropriate operating point.

So the draw will depend on how you design your lighting system.  Series, parallel, drive scheme and target current.