I would disagree about Misaki just being able to kill what she wants, except of course, on that *shudder* recalled training *shudder shudder* turn. However, she can pick her fights better than anyone in malifaux. I'm aware assassinate was in the pool, but make Lady J a fight she just won't want to pick. Bring along a defensive piece to buddy up with her, such as sidir, francisco, or the guardian, or even all three. Remember her defensive trigger - an opponent that's been stung by it once will never again take charging Lady J lightly.
As for the thunder archers, that upgrade can be mad if you don't plan for it. In general, give them a hard time shooting you. Don't bunch up for their blasts, skirt around terrain, mash your dudes into melee at the first opportunity and so on. Remember that they are trying to outshoot the guild - don't let them. Your guns are often just as damaging and accurate, but there are more of them and they are more likely to be somewhere you want them to be. That, and those archers have five wounds and the same defense as a paper bag. Riflemen have the same range and with the right support can ruin them with one shot, too. Finally, there is a weak point in hail of hachinosu; the holder of the upgrade. Kill them (presumably with bullets) and the archers lose half their effectiveness.
Other general advice for Lady J - Vendetta style is always very yes. Executioners are hard to use, easy to kill and don't perform without bringing support for them (such as mcmourning's buffs, mccabe's upgrades, promises from sidir, boxing them with a marshall etc), so I'd steer clear in Justice lists. Can't see the rationale in taking the lawyer and witchlings, save from them being pretty nice in general, but better synergy is to be had elsewhere. Guild can own reconnoiter handily if they bring decent shooting. In general, Lady J isn't a master you want to bring along if there's assassinate in the pool. She always gets beaten to a bloody pulp mid-game, or you're not doing the right kind of damage and disruption with her early on (my opinion, mileage of others will almost certainly vary).