I believe the estimates for how long Lake Vostok water has been isolated cap out at around 25 million years. Although that is an incredibly long time, it isn't anywhere close to long ago enough to ensure a sterile condition when it was first isolated (It would need to be several billion years to proceed life as we know it already blanketing the planet).

As I understand it, the prevailing notion is that abiogenesis happened only a single time, or at least only a single time that stuck. The life that already exists does a pretty good job of ensuring that any primitive re-developed life never has a chance to actually get started. You would need to completely sterilize the environment to have a shot at witnessing abiogenesis again. Maaaybe all life in the lake died, rendering it sterile, and then new life formed, but that seems super unlikely to me. Why would the existing life die if there was enough nutrients/energy to allow new life to form? (Also, 25 million years is probably far too short of a timeframe to see abiogenisis bootstrap DNA based life)