Have you tried just eating a very small meal beforehand? Sometimes I have a handful of nuts or half a tangerine (food I feed to my parrots) or even a very small bowl of plain yogurt. Mostly I go in before breakfast and eat right after. I only get dizzy because the weight is heavy, not from low blood sugar. I sometimes get really super hungry, and then my breakfast feels awesome to eat.
Female, 5'3", 49, Starting weight: 163lbs. Current weight: 135 (more or less).
Starting squat: 45lbs. Current squat: 170 x 3. Current Deadlift: 220 x 3