Does anyone have a datasheet for this Arira LCD

It's likely to be the GC1604N0, which is the only textual 16x4 display now available by Goldentek.

Note that the part number you found seems not to be consistent with the usual coding of the manufacturer, as they use GC* instead of LM*.

Here there is their coding standard, which seems not including the 'LM*' code.

For understanding the interface you can try to use the block scheme, in which the pins should be displayed in the right order. The problem is that the board has 16 pins while the scheme shows only 14 lines: trying to find where is the supply turning the backlight on may be a way to go.

From Microtypes Website, Naming System:
Type of Display: MTB Board assembly & Custom design
LCD Type: F: FSTN
Development Number: 000393 (Assuming Customer Reference)
Polarization Type: F: Transflective
Background Color: G: Gray
Operating Temp.: H: Extended Operating: -20° C ~ +70° C Storage: -30° C ~ +80° C
Viewing Direction: S: 6 O'clock
Backlight: A: Array LED
Backlight Color: Y: Yellow Green
Sub Code: A (Special, no information available)

You don't mention how many characters it is, just that it is 2 row. Considering that all of their stock characters LCDs use 16 pins (or less, I've gone through each pdf), it's hard to guess at the pinout. The options are Do you still have the broken device? You could use a multimeter to figure out vcc and gnd, maybe even the led control, and once you have those, it could be easier to figure out the data pins.

For the most part, they only have hd44780/splc780/KS0066 compatible lcds in their standard character stock, I'd be surprised if their custom parts deviated too much from it (or that the customer wanted/needed something too far off from the standard)

You could always email Microtips and ask. It never hurts.