You do NOT receive a W-2 if you are a Self-Employed Uber or Lyft driver. You will receive a Form 1099-MISC for your income.
ALL income received in 2019 MUST be entered on a 2019 tax return. NOT on some future tax return.
See this TurboTax support FAQ for Uber/Lyft income - https://ttlc.intuit.com/community/uber-or-lyft/help/where-do-i-enter-my-lyft-uber-income/01/26804
...AND...You save those 1099-MISC forms (and W-2 forms if you have other jobs) for at least 10 years. Each in the tax-year folder that you save your copies of that year's tax returns. You need to save them for a number of years, because the IRS (and State) does ask questions, or audits random tax returns long years after you filem (usually within 3 years, but not always). Once you lose them, you have no proof of income for that year (and what's in the software is not sufficient proof of income)