How to Sustain Alertness I am wondering if alertness is best sustained in terms of:


Attempting to sustain alertness in meditation, not meditating when too lethargic. In other words, always exerting oneself and keeping sharpness when in meditation, and stopping when the mind becomes unclear.
Or, engaging with meditation even when lethargic, continuing one's meditation despite the mind being unclear and hazy. In other words, waiting for the mind to clear up. 


Which is more accurate?
Your meditation method cannot to be too comfortable, nor too uncomfortable, that is why people mostly choose to sit in half or full lotus with straight back so they don't slouch and sloth. Be careful not to slouch, keep back upright, work on posture and correct it.

Question 1:


  Attempting to sustain alertness in meditation, not meditating when too
  lethargic. In other words, always exerting oneself and keeping
  sharpness when in meditation, and stopping when the mind becomes
  unclear.


Sustain, but gentle mindfulness or awareness, I wouldn't say alertness as it implies stress as in fight or flight type of thing. Note that you are feeling lethargic. Do not stop, note that mind becomes unclear. Eventually correct your posture, straighten the back and continue. It is generally to be mindful of it just to the extent of eating, or waking up (both in meditation and daily life)


  Again, bhikkhus, a bhikkhu is one who acts in full awareness when
  going forward and returning; who acts in full awareness when looking
  ahead and looking away; who acts in full awareness when flexing and
  extending his limbs; who acts in full awareness when wearing his robes
  and carrying his outer robe and bowl; who acts in full awareness when
  eating, drinking, consuming food, and tasting; who acts in full
  awareness when defecating and urinating; who acts in full awareness
  when walking, standing, sitting, falling asleep, waking up, talking,
  and keeping silent. 9. “In this way he abides contemplating the body
  as a body internally, externally, and both internally and externally …
  And he abides independent, not clinging to anything in the world. That
  too is how a bhikkhu abides contemplating the body as a body


Question 2:


  Or, engaging with meditation even when lethargic, continuing one's
  meditation despite the mind being unclear and hazy. In other words,
  waiting for the mind to clear up.


Engage, yet gently noting haziness and confusion, lack of clarity. Eventually correct your posture, straighten the back and continue.

On mental hindrances, such as:


Sensual Desire
Ill-will
Sloth and Torpor
Restlessness and Remorse
Doubt


https://www.accesstoinsight.org/lib/authors/nyanaponika/wheel026.html

Bonus: "Is there such a thing as bad meditation?":