Yes, there is evidence that just this happened 210 million years ago a temporary lake on the flanks of Arsia Mons, possibly two lakes of around 40 cubic kilometers of water, and a third one of 20 cubic kilometers of water.
Also if a comet like Sliding Spring hit the polar regions of Mars, it would create a temporary lake covered in ice. It would keep hot for some time partly by the hydrothermal vents the impact would probably trigger. Heated by the melted rock from the impact fed by underground aquifers to create a hydrothermal system.
In both cases they would stay liquid for thousands of years. Not quite the millions of years of lake Vostok, but still, a very long lived lake below the ice.
So - not formed in quite the same way as lake Vostok, and also - I don't think it would be an oxygen rich like lake Vostok - but - otherwise a similar type of habitat, hydrothermal vents (they expect hydrothermal vents in lake Vostok also, as quite likely) and completely cut off from sunlight.
For more about this - I've got a short summary of the research in this draft article I've done for wikipedia, which has links to papers to find out more: Draft:Present day habitability of Mars
In both cases they would stay liquid for thousands of years. Not quite the millions of years of lake Vostok, but still, a very long lived lake below the ice.
So - not formed in quite the same way as lake Vostok, and also - I don't think it would be an oxygen rich like lake Vostok - but - otherwise a similar type of habitat, hydrothermal vents (they expect hydrothermal vents in lake Vostok also, as quite likely) and completely cut off from sunlight.
For more about this - I've got a short summary of the research in this draft article I've done for wikipedia, which has links to papers to find out more: Draft:Present day habitability of Mars
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Robert Walker
Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.Studied at Wolfson College, Oxford
Lives in Isle of Mull
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