The problem with both Lyft and Uber is they have MASSIVE VC investments they need to pay back, and while the business model is good its not nearly good enough to payback VC within the 10 year window. Uber will be in the exact same boat next year.
What do you mean "pay back"? If you're talking about liquidation preferences those all go away in an IPO.
All the investors that 'purchased' a percentage of the private company with their investment during funding rounds will want to see ROI when the company goes public (or if the company is insanely profitable while private). Most of these VC's expect to start seeing ROI around the 10yr mark. The company isnt remotely profitable still privately held, so lets go public and get other suckers to buy in so the early investors can cash out and hopefully make a buck or two or at least breakeven.
It's not the companies (and their earnings) who will pay back investors. Other bagholders will do that once they go public.