If the ropes are doing negative work on lift, why is electric energy needed? And why is there a limit on number of passengers in a lift in this case?? Please explain in terms of energy conservation and Work Energy Theorum
When an elevator is descending what is needed is a mechanism for getting rid of the gravitation potential energy of the elevator.
A very inefficient way would be to have a friction brake with heat being generated as the elevator descended.
One way of helping to improve efficiency is to have a counterweight, which could be another elevator, so the potential energy from one elevator going down is transferred to the counterweight going up.
The potential energy of the counterweight (often weighing the same as an elevator loaded to $40\%$ capacity), can then be used to raise the elevator.
This reduces the amount of work which the motor has to do and so increases the efficiency of the system.
This system was used 100s of years ago allowing fully loaded mineral trucks from a mining operation to go down a hill whilst empty trucks were hauled up the hill.
There are systems where the motors are regenerative so that they not only do work but can have work done on them thus acting as a generator (and a brake) and producing electrical energy for use in other parts of the facility.
The article Energy efficient elevator technologies gives some more information about improving the efficiency of elevators.
It is a matter of control of velocity, the correct acceleration going up, and the correct deceleration going down that need electrical power.
There are the counter weights, but the load is variable in the elevator and that has to be taken care of with the power from electricity, whether ascending or descending. With just the counterweights nopower is needed either up or down!!