Lotus Trap

Yes. When damage is assigned in the combat damage step, a replacement effect that would apply to the resulting damage is considered to apply to the assignment instead, so Lotus Trap's doubling takes effect as damage is assigned — not only when it is dealt.

Assigning damage and dealing damage are still distinct steps.^{[465.2.c.1][465.2.c.1.a]} But the rules fold damage replacement effects into the assignment step: any replacement effect that would apply to the resulting damage is applied to the assignment.^[465.2.c.5]

A unit must have lethal damage assigned to it in full before any remaining damage may be assigned elsewhere,^[465.2.c.3] so the doubling changes how much of the attacker's damage the unit ties up. The assigning player picks the smallest raw amount that, once doubled, reaches lethal damage — for a 3 might unit under Lotus Trap, assigning 2 raw damage doubles to 4, so only 2 need be committed to kill it.^{[465.2.c.4.a]} When damage is finally dealt it is not doubled again, since the doubling already happened during assignment.^[465.2.d]

If more than one replacement effect applies to the unit — for example a prevent effect alongside Lotus Trap — the unit's controller chooses the order they apply during assignment, which can change the final assigned and dealt amounts.^[465.2.c.5]