Both low beams not working,

You can't use High Beams as dipped, the spread is different. Just go to another garage, it can only be the bulbs, the connection, the fuses or the relay. In fact you can check all those yourself! It appears to be a known issue on the Impala. Look at the videos

https://www.google.com/search?q=2000+chevy+impala+headlight+problem

Fuse Box Diagram Chevrolet Impala (2000-2005)

https://fuse-box.info > chevrolet > chevrolet-impala-20...
It is located on the passenger's side of the instrument panel, behind the cover. The location of the fuses in the passenger compartment: Chevrolet Impala (2000- ...

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Possible problem is at bulb plug in. Take & disconnect the light from wiring connector, put DIELECTRIC grease in wiring plug after you check for corrosion. Sometimes it gets a film on connections & just need some TLC... GOD BLESS.....

The headlight relay provides power to the dimmer relay, then power goes thru a fuse for each light for each circuit (4). The low beam fuses are in fuse block 2. The dimmer relay is controlled by the daytime running light module. The headlight and dimmer switches send signals to the DRL module. You may need a shop manual to troubleshoot the circuits.

Check bulbs. had this happen on my intrigue had no high beams but lows worked. If bulbs are fine check fuses and relays.

follow the wires back and see if it rubbed on metal and the wire is broken

I work for a chevy dealer I will look into the problem and get back to you.

check the relay/fuses

I would say your light switch is either dirty or bad.
www.rockauto.com

sounds like the problem is the dimmer switch, get a price on the dimmer switch. If you have to, get one at a junk yard . It's cheaper.

High and low beams use different bulbs. Both of my low beams blow out at the same time. Replace the low beam bulbs.