LA definitely treats the water. Both the surface water before consumption (I'd be surprised if any city doesn't do this) and the wastewater, for reclamation for nonportable use like irrigation, and for recycling back into the general clean water supply.

The aqueduct water is specifically purified by the Los Angeles Aqueduct Filtration Plant. That plant is gravity fed, but it doesn't operate without power.

LA just has the advantage of having mountains in the city, so it's cheaper building more elevated water storage so the capacity lasts longer during power interruptions (which are also not as common or extended as they are in the east). They will still eventually run out if they're not replenished by powered pumps.