Other than occasional, one time promotions and bonuses you are going to have to pay the cost of someone driving you where you want to go. That includes the costs of operating the vehicle, the cut Lyft Takes, and profit to make it worth the driver's time.
Its naturally going to cost more than driving your own vehicle because when you drive yourself you aren't paying a driver for their time and you aren't paying a middle man (in this case, the Lyft corporation) a service fee for connecting you with the driver.
You could ask friends, family, neighbors and coworkers if anyone drives a similar route and offer then $7 per day to drive you - effectively cutting out the middle man.
Or perhaps you should put the repair on a credit card or get a small personal loan to get your car back, and then use the money you save by not hiring lyft everyday to pay off the debt.