Mac Zero: *There is never any good reason to operate your MBP with the battery removed.* Doing so does not prolong the life of the battery or the computer, and the computer's clock speed is automatically reduced by half when you do so. That accounts for the lag you are seeing. It is intentional, because when the computer is working extremely hard it may require more power than its AC adapter can provide, and it's designed to draw the additional power it needs from from its battery under those conditions instead of tripping the overload protection in the AC adapter, which would cause the machine to shut down without warning if the battery were missing. Slowing the CPU when the battery is removed reduces its maximum power demand to what the AC adapter can safely provide.
Once the battery is fully charged, charging stops and does not begin again until the charge level drops to 93%. This allows the battery to remain cool most of the time even if the AC adapter is nearly always connected and the battery remains in place. Apple's smart charging algorithm also limits the heating of the battery and the adapter even while it is being charged, by varying the rate of charge throughout the charging cycle.
In short, leave your battery in place at all times. Your MBP will perform better in everything you use it for, you will lose nothing from your battery's useful lifespan, and you will never lose data to a power outage.