The vertical component of Lift has to match the force of Gravity, otherwise you accelerate downwards.
A number of previous posts revolved around this issue: How to reconcile the vertical component of lift with gravity, so that vertical acceleration is zero.
The missing link is not in tweaking the lift vector, but in the fact that there is now a vertical component to the drag vector. And since engine power is reduced (or absent, in the EFATO scenario) this vertical component of drag is not offset with the (downward) vertical component of thrust.
In the very extreme case, for instance a skydiver free-falling at terminal velocity, this is the only force that keeps the skydiver from accelerating vertically. (In other words his vertical speed is constant.)