In fairness, should they? It was your vehicle, insured by the carrier of your choice, with the coverage and cost tradeoffs of your choice. I would certainly expect Lyft to pay enough to make it worthwhile after all costs, including fuel and insurance. But should they be on the hook for the actual repair costs? If so, for how much? Should they repair a brand new Mercedes the same as a 20 year old Honda?

I get some of the drawbacks to gig-based work, but I think you have to realize that it does enable options that wouldn't exist in traditional employment scenarios, and SOME of the risk does remain with the contractor. No, I'm not saying Lyft has no responsibility in any situation, but getting into a garden-variety accident while on the road definitely sounds like a situation that's within the envelope of known risks when you decide to do this kind of thing on a gig basis.