Everything in this answer is taken from the website of the Láadan language (link to the page). I am by no means an expert, but this is directly from the mouth of Laáadan's creator. The following quote contains pertinent excerpts of the article, parts of which I have put in bold:
Another goal I had for Láadan was that it should be as easy as possible to figure out what a particular word or morpheme means just by looking at it...I wanted the language to work like a Tinkertoy® set works, so that people could take the pieces and fit them together easily to make larger forms. For example: the Láadan word for “bee” is “zhomid”; that word is made from “zho” — the Láadan word for “sound,” and “mid” — the Láadan word for “creature.” The meaning is transparent from the word’s parts.
First, however, I had to construct the most basic elements of the language — the words/ morphemes that are called “roots” and can’t be taken apart into smaller meaningful pieces. When linguists begin working with a language for which no grammar or dictionary is available, they ordinarily start with a set of roughly 100 very basic words made up of items like “eat” and “sleep” and “food.” I followed that practice, and began by constructing a core vocabulary of those basic words; when I had those done I began adding additional roots that I felt were needed. Sometimes I can explain to some extent how I chose a particular shape for one of those words; much of the time I can’t.
For example… I can explain that I chose “oódóo” for “bridge” because when pronounced its tune makes the shape of a humpback bridge. I can explain that I chose “rul” for “cat” because the purring of a cat sounds to me like “rulrulrulrul…” But the choice of “ana” for “food” and “ina” for “sleep” was arbitrary; I have no explanation for those choices other than that I tried to give them a shape that could easily be combined with other morphemes. For any constructed language that isn’t based on some existing language, the hardest part will always be putting together the inventory of roots.
An update to the Láadan dictionary shows that not all of the words were created by Suzette Haden Elgin (the creator of Láadan) but all that are not roots in and of themselves--roots which seem to have been created rather arbitrarily--can be figured out from these roots. For example, in the dictionary I linked, the word for beaver is "eduthemid." This contains the rood for animal, "mid," and some other root, I presume "eduth." I do't know what this means, but it was constructed in this way so that someone who knew these roots but did not know the word could discern that it means beaver.
The original creator of Láadan made a couple of arbitrary roots that could then become a lexicon through a logical process of morphology, with help from multiple other people.