Halo orbits are a sub-class of Lissajous orbits. See this answer for (much) more on that.

DSCOVR's orbit will put it in it's Sun Exclusion Zone in about 2020 where the communications line of sight will be too close to the Sun, so there is a planned orbital correction there to handle the situation. You can see from the image the insertion point labeled LOI, and about a dozen cycles in five years. The horizontal and vertical periods are almost the same for this orbit. From Lissajous Orbit Control for the Deep Space Climate Observatory Sun-Earth L1 Libration Point Mission

After 2020, DSCOVR will then have to burn fuel every 3 or 6 months to stay on that exclusion zone-riding ellipse. The linked report predicts that fuel will run out around 2028.

DSCOVR's Lissajous orbit

Question: Why couldn't Triana have her halo orbit, and therefore a much longer continuous-coverage life? Why is DSCOVR in a Lissajous orbit instead of a halo orbit (to stay out of Sun exclusion zone)?

There is relevant discussion in answers and especially comments associated with Why would a mission to Sun-Earth L1 have an instantaneous launch window?

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