Help selecting rechargeable batteries for 3W 1A handheld lantern
Lithium or the much safer LiFePO4 would be appropriate here, certainly not non-rechargeable D cells. There are larger cells than 18650 ... a couple of 32650 cells might be more appropriate.
1 LiFePO4 cell (3.2V) covers a range of 3.6V (very briefly), 3.3 to 3.1 (most of the discharge time) ad can be used down to 2.5 but there's no point going below 2.8V. Unfortunately this probably crosses the voltage range of your LED so you either need a buck-boost converter, or (probably better) 2 cells in series and a buck converter.