From Modern American

The name Lamoine appears to be a rare, modern, regional, surname-based, or creatively spelled name, and a widely documented traditional meaning is not clearly established. For names like Lamoine, the safest interpretation is to treat the name as a distinctive contemporary form rather than assign it an unsupported ancient origin. If the name resembles a known root name, place name, family name, or cultural form, its meaning may be connected to that source, but the exact meaning should be considered uncertain unless supported by family, cultural, or linguistic context.