Otherwise known as a Funicular
Not only would a North-South LRT save the air from fossil-fuel burning buses climbing up and down the hill all day long, but in addition the escarpment portion of the route would incorporate an inclined rail system. Yes it can. Imagine sitting in an LRT car as it pulls up to the bottom of the Claremont access, and you feel a gentle engagement of the lifting mechanism as one does when on a roller coaster before being hauled to the top of the ride. It is paired with a car at the top coming down.
In such a system the downbound train at the top of the escarpment would engage with the upbound train at the bottom via pneumatics, hydraulics, or just a plain cable. The mass of the train rolling down the hill offsets the mass of the upbound train, thus significantly reducing the energy input required to move the trains, theoretically close to zero.
Zero energy to travel up and down the escarpment? Why haven’t we done this before? Oh yeah, we have.