How to work out lifting capacity of a motor with a power rating in newtons?
A motor rating in Newtons makes no sense.  That's the same as rating your car engine in pounds.  Perhaps this "motor" is rated for the weight of garage door it can lift with the mechanical system of a particular model around it.

Before you are ready to spec a motor, you have to find the power your dumbwaiter needs.  Decide the maximum loaded weight of the whole mechanism, and then the maximum time you are willing to let it take to get from the lowest to the highest points.  The force that must be applied to the dumbwaiter mechanism times the distance is the total energy required to lift it.  That divided by the time you want it to take is the power.  Of course there will be friction losses, so the power input to the mechanism must be higher.  I'd add at least 50% extra.  No matter what else, the motor must be rated for at least this much power, else it simply can't perform the task.

The other degree of freedom that must be specified for the motor can be expressed as the torque it puts out at the desired power.  The mechanical linkage between the motor and the dumbwaiter mechanism converts the torque from the motor to a force on the dumbwaiter.  You have some leeway here since this mechanical mechanism can be made with a reasonably wide ratio.  You need to know what the motor torque is to pick the ratio, but you can work with any motor torque within reason, as long as the motor can supply the power.