About led connection
It is going to work fairly well.  You may want to use two batteries in parallel. You may want to drop the resistor value below 5Ω so the LED is brighter as the battery discharges.

Most Li-ion are 3.6V nominal and many vendors of off brand batteries claim they are 3.7V.  They charge to 4.2V buy quickly drop to below 4V.

The closest common resistor to 5Ω is 5.1Ω.

At 3.6V with a 5.1Ω current limiting resistor the current is 120 mA, power dissipation is 432 mW, and efficiency is 83.3%.



x20 LEDs = 2400 mA





A popular Li-ion is the Panasonic NCR18650   

You are looking at about a 1C discharge which is shown in the datasheet in the Discharge Characteristics (by rate of discharge) as the green curve. 

   

As the battery discharges the voltage tapers off and the efficiency improves.

When the battery is at 3.1v, approaching its cutoff voltage, the the efficiency is at 96.8%.  The bad news is current drops to about 20 mA. 







I would use a 4.3Ω which would slightly exceed the 150 mA for the first few minutes after a fresh charge but would remain brighter longer. A 4.7 is the maximum I would use.  A 5.1Ω will work okay.  

You could use a boost CC driver with a 30V output and wire the LEDs in 10 sets of 2 parallel LEDs in series.

I do not use boost converters or buy off the shelf.
These circuits are made for powering mobile device LEDs and screens. 

What the boost converter will do for you is give you consistent brightness from fresh charge to cutoff. It may not give you longer battery life.
The resistors are fairly efficient.  The boost driver will keep the output power constant where the batteries will discharge and lower the output power (and brightness).   

TPS61500 3-A Boost Converter
Microchip MIC2299

If you were to search for an off the shelf use the search term "boost step up constant current"
You need 3A (2.4 Amp minimum) with 3V or less input.