Powering an LED with a battery and using a current limiting resistor is not recommended. Especially for a lantern where you want a more consistent luminous output.
You could use a buck/boost DC-DC converter to keep the voltage consistent and adjust the output voltage for a high efficiency current liming resistor.
You must first measure the actual Vf then adjust the output voltage
The TI High Efficiency Single Inductor Buck-Boost Converter TPS63030DSKR was made especially for this type of application (i.e. battery powered white LED).
I'm connecting two 3V CR2032 Lithium batteries in series.
A CR2032 has a capacity of only 235 mAh and that capacity is for a much lower load than 700 mA, if you can get 700 mA.
Source: DATASHEET ENERGIZER CR2032
with your proposed design the LED will light up for a few minutes then dim to 20% of the original intensity a few minutes later.
I would recommend using Panasonic or Samsung 18650 Li-ion cell(s).
An LED being driven with 700 mA will need some thermal management. You may do better with a higher efficacy LED driven at a lower current.
Your Vf of 3.5V is too high. I recommend the highest efficacy LEDs available today (August 2018)
- High power Cree XP-G3 (2.7V-3V) or
- Mid power Samsung LM301B (2.6V-2.9V)
A constant current regulator made for battery operation is recommended. This does not work with your 6V battery. This circuit was designed for a single or dual cell supply (e.g. AA, NiMH). With this circuit the battery voltage should not exceed the LED's Vf
Very simple inexpensive ($1 single qty) made to drive a single white LED.
0.5V - 5.0V input, 5.0V, 550 mA output.
Works well with mid and high power LEDs.
MCP1643 is a compact, high-efficiency, fixed frequency, synchronous
step-up converter optimized to drive one LED with constant current,
that operates from one and two-cell alkaline and NiMH/NiCd batteries.
The device can also drive two red/orange/yellow series connection LEDs.