to react with later for 
UncommonDoes Lotus Trap affect how much damage needs to be assigned in combat?
Yes, Lotus Trap's doubling applies while combat damage is assigned, so the assigning player uses the doubled amount to determine lethal assignment. A replacement effect that would apply to the resulting damage is considered to apply to the assignment instead.467.2.c.5
Assigning damage and dealing damage are still distinct steps.467.2.c.1 A unit must have lethal damage assigned to it in full before any remaining damage may be assigned elsewhere,467.2.c.3 so the doubling changes how much of the assigning player's damage the unit ties up. For an undamaged 3 unit under Lotus Trap, the minimum is 2 damage: assigning 1 doubles to 2 and is not lethal, while assigning 2 doubles to 4 and is lethal.467.2.c.4.a When that damage is dealt, it is not doubled again because the replacement was already applied during assignment.467.2.c.5
If another damage replacement also applies, the unit's controller chooses their order during assignment, which can change both the assigned and dealt amounts.372467.2.c.5