Uber Technologies Inc. and ridesharing rival Lyft Inc. are racing toward an initial public offering—and neither company’s general counsel has gone public before.

Uber CLO Tony West joined the San Francisco-based company from PepsiCo, which was already public when West came on board. His Lyft counterpart, Kristin Sverchek, joined the company in 2012 with a background in M&A and no experience at a public company.