I think LapPacks should be able to recharge NanoSuit Armor. This makes sense because they can recharge the Nano Saber as well as other equipment that can be charged in a BatBox or MFE Unit. While wearing a LapPack, if you're wearing a NanoSuit Helmet, NanoSuit Leggings, or NanoSuit Boots, they would be recharged when you take damage.
Since you can't wear NanoSuit Bodyarmor if you're wearing a LapPack, this obviously wouldn't work for NanoSuit Bodyarmor, so you wouldn't be able to use a complete set of Nano while wearing the LapPack. Also, since QuantumSuit Armor can only be recharged in an MFS Unit, you shouldn't be able to use a LapPack to recharge QuantumSuit Armor.