My theory as to the informal use of the rank of "Lieutenant-Major" is ingenious but has no historical support that I can discover. If the rank had existed, Kochler (the historical one), would in any case not have held it during his expedition with Moore, as it would have only been relevant had he been a Lieutenant acting as company commander for his Major. But he was a Captain, so, if on regimental duty, would have had his own company.