five_corparty: A Mercenary 'mech lance includes it's own organic support. When you factor in all of that, it's really a company, and "Captain" is appropriate. House forces will have those support elements under other command arrangements.
I'd argue that, for purposes of discussions, we have to use the terms as they are intended: a lance is a lance, a platoon is a platoon. Sometimes the platoon might have six vehicles (like in Marik space) but it's still a platoon. For purposes of discussions, if someone says "a BattleMech lance commander," we can't say, "oh, and a bunch of other stuff that's invisible and assumed." In the game and fiction, you're right, a lance always has support elements. But for discussions, I think clarity is better: Lord knows people argue enough when things are clear, no sense muddling the language. ;)
That said, however, a Captain is 100% appropriate for a combined arms company, which is what you're describing. And I also DO see said unit being hired as a "BattleMech Lance" because that's what the employer wants, and a lance with support elements (theoretically) would be cheaper than "combined arms company."
...In fact, that might be how that custom came about! Because employers pay less for lances, they tended to hire that way, and units either learned to advertise as the employer wants, or get left behind as the employer goes for the "lowest bidder."
Hmm- not canon, but logical...