The L2 has two sections of tube. If you use both, you can fit two batteries in series. That would give you 6-8V. There's no way, in that host, to get two batteries in parallel for 3-4V. That's the voltage sent to the driver. The driver determines what gets sent to the LEDs.
Almost all LED drivers are either current regulating (meaning that they control the current sent to the LEDs) or direct drive. A direct drive or FET driver simply connects the battery to the LEDs with as little in between as possible. These drivers depend on the resistance of the batteries, LEDs, FET, and wiring to limit the current to a safe level.
The LED board you linked to is designed for only 80 mA, so you definitely want a current-regulating driver. A FET or direct drive driver would probably fry the emitters in a second or less on fully charged batteries, even low-current ones.
80 mA is a pretty low current for flashlight drivers. While there are many that can be dimmed to that level, or even well below that, you'd want to make sure it NEVER came on at full power. There are few drivers that have a max of less than 350 mA, and that could easily destroy the emitters before you knew something was wrong. There are some however, that have a resistor that can be changed to adjust the max output current.
I usually make my own drivers, so I don't follow the commercial world very well. If there's a good driver out there for you, I'm not aware of it. What you need is a low dropout buck or linear driver with a sense resistor you can change to adjust the output current. Maybe someone will suggest a good one for you. Usually people are interested in changing resistors to increase output, but you want to decrease it, but that shouldn't matter.
I actually have made and sold such a driver, and while I haven't sold one in some years now, I could easily make you one with a single 80 mA mode. It's rather spendy and massively overkill for what you want, and I'm not sure it would fit in the L2, but if so I think it would actually work pretty well. Post in this thread if you are interested.
https://www.candlepowerforums.com/v...table-10A-linear-LED-driver-New-and-Improved!