First off, notice that
exactly eight letters (DGKORSUW) occur in first place, and exactly four (AIMN) in second place. That's already a bit suggestive. And, wait, that set of four looks familiar: they're the letters with length-2 Morse encodings. And, indeed, the first-place letters are exactly the letters with length-3 Morse encodings.
we are dealing with five-bit strings, which are operated on by our weird symbols, and at the end of each row we turn them into symbols by mapping each bit to one segment of the "5-segment LCD display".
What do those weird symbols do, exactly?
It looks, from the given examples, as if FIRE is exclusive-or, TOADSTOOL is bitwise-and, BLUE-THING is bitwise-or; RAINBOW is cyclic-shift-left, SPARK is bitwise-not, and TREE is cyclic-shift-right. For reasons I cannot guess, I initially thought that the cyclic shifts were within each letter rather than of the whole 5-bit value -- in the examples given, these all yield the same result. This gave me gibberish after the first couple of rows. Thankfully, user ttotherat spotted that shifting the whole thing makes everything work.
For instance, consider the first row.
We start with OM = --- -- = 111 11.
Then we do FIRE (i.e., XOR) with UM = ..- -- = 001 11, getting 110 00.
Then we do TREE (i.e., right-shift), getting 011 00.
Then we do SPARK (i.e., not), getting 100 11.
Then we do TOADSTOOL (i.e., AND) with OA = --- .- = 111 01, getting 100 01.
Then we do BLUE-THING (i.e., OR) with RA = .-. .- = 010 01, getting 110 01.
Numbering our bits 1..5 from the left, that's bits 1,2,5.
That means the left, top, bottom segments.
That gives us a letter C.
Very nice so far. The next row
gives us a letter O,
also very reasonable. And with the boneheaded mistake mentioned above corrected, as user ttotherat has found, we get
COCIBOLCA, also known as Lake Nicaragua.
Credit where due: ttotherat spotted an idiotic thing I'd done and found that if you do the should-have-been-obvious less idiotic thing you get an answer that makes sense, rather than the gibberish I got. If you like my answer, please consider upvoting ttotherat's.