A pair of court rulings involving Lyft Inc. and Uber Technologies Inc. may have far-reaching consequences for the ride-sharing firms, and may help to bring clarity to a murky but increasingly important area of employment law.

Two San Francisco judges separately ruled last week that suits filed by drivers of the ride-sharing services should go before juries. At issue in both cases is whether drivers, who are employed as independent contractors, should be considered employees of those firms, and thus entitled to the protections...