Hi GreenAir, welcome
I think this is probably the best place to find e-cig modders building stuff from the ground up.
Flashlights and e-cigs have a lot in common as far as power requirements. Higher end flashlights typically use 10 to 20 Watts over a range of voltages above and below the voltage of a single Li-Ion cell. So do e-cigs.
Yes, LG Chem makes Li-Ion cells. They've been making Li-Ion cells just as long as companies like Panasonic and Samsung. You don't see them much at the retail level, but the LG cells are used quite a bit in laptop computer packs.
The LG ICR18650 D1 is a really amazing cell. It has the lowest internal resistance of any ICR 18650, I've bench tested about 66 mOhms. Other ICR 18650 cells are typically 80 to 100 mOhms. That and the higher operating voltage means more power delivered to your appliance.
That higher operating voltage is both its advantage and its disadvantage. The advantage is the cell has higher energy density. In terms of energy, the ICR18650 D1 carries just about as much as a Panasonic NCR18650B even though the LG cell has 3000mAh compared to 3400mAh for the Panasonic cell.
The down side is you need a non-standard charger for the LG cell. It uses a terminal charging voltage of 4.35V compared to 4.20V for a standard Li-Ion. Removable round cell chargers like that are not available. Though, you can find charger controllers with a 4.35V terminal charging voltage then make a USB charger adapter. It's what I've done for the e-cig mod I use them in. The LG cells perform impressively.
Oh, that board is of my own design. It carries a 36 Watt booster, an MCU that controls everything including a display, and a USB charger. I've been building e-cig mods for a few years now and that board has evolved over several iterations. The one pictured is probably going to be my final design. I don't think I can improve the function or reduce the size any more than I have.