This name is not immediately suggestive of an etymology. Perhaps something like the root suggested for LAMAN, with the second vowel a changing to an o by the Canaanite shift (/ā/>/ō/), and with 1c.s. pronominal suffix /ī/ or a gentilic ending /ī/.
Reynolds & Sjodahl first connected LAMONI to LAMAN, though without explaining how the two were related (R&S, 26). The connection was made again, but this time the gentilic ī ending was suggested (JAT & RFS), similar to the gentilic “ISRAELITE.”
Deseret Alphabet: 𐐢𐐁𐐣𐐄𐐤𐐌 (leɪmoʊnaɪ), 𐐢𐐁𐐣𐐃𐐤𐐌 (leɪmɔːnaɪ)