What should I be eating before and after an intense workout?

You could try some medium chain triglycerides (like coconut oil) if you feel sluggish, it's readily converted to ketones and could help with the dizziness if it's related to exercise using some of the ketones the brain would usually use. It takes a few days to get used to, so try it when you have access to a bathroom.

You could also try some protein if it's a problem with low blood sugar (could help through gluconeogenesis, and would probably spare lean mass).

I posted this in another thread:

Try to eat some Spinach and/or some Avocados (calcium/magnesium/potassium), and swap out your regular salt for mineral salts (contains magnesium/potassium). Both mild magnesium and potassium deficiencies have fatigue and muscle weakness as symptoms.

The diuretic (dehydrating) nature of ketosis causes an excretion of three of the body’s primary electrolytes: sodium, potassium, and magnesium (31,40). These three minerals are involved in many processes in the body, one of which is the regulation of muscle contraction, including the heart. Some studies show a net loss of calcium while others do not (31).

"The Ketogenic Diet" by Lyle McDonald, page 79.

It takes a few weeks to adapt to the diet, I posted this in another thread (there's some details in the follow-up posts also):

It can take up to three weeks for your muscle to adapt and stop using ketones when glucose is sparse, it might be that if you do intense exercise the energy need of the muscle will surpass the amount of ketones being created, and I'm guessing you could get the same "bonk" (but I can't really verify that):

As described previously, muscles will derive up to 50% of their energy requirements from ketones during the first few days of ketosis. However this drops rapidly and by the third week of ketosis, muscles derive less only 4-6% of their energy from ketone bodies (22).

"The Ketogenic Diet" by Lyle McDonald, page 46/47.

After that period your performance is limited by the available fatty acids and not ketones (ketones are made from fatty acids, mostly, by your liver). The definite time it takes to adapt might vary, but a study over six weeks show that people can still increase their endurance on Keto during that time frame:

To study the capacity for moderate endurance exercise and change in metabolic fuel utilization during adaptation to a ketogenic diet

...

The duration of treadmill exercise to subjective exhaustion was 80% of base line after 1 wk of the PSF, but increased to 155% after 6 wk.

Phinney SD, et al. "Capacity for Moderate Exercise in Obese Subjects after Adaptation to a Hypocaloric, Ketogenic Diet" J Clin Invest. 1980 November; 66(5): 1152–1161.

Looking at another keto endurance study in well-trained cyclists shows an increase at the fourth week of keto (EBD = eucaloric balanced diet, EKD = eucaloric ketogenic diet, EKD-4 = week four of keto):

The mean ergometer endurance time for continuous exercise to exhaustion (ENDUR) at 62%-64% of VO2max was 147 minutes at EBD-1 and 151 minutes at EKD-4.

and..

Neither clinical nor biochemical evidence of hypoglycemia was observed during ENDUR at EKD-4.

..

This was accomplished by a dramatic physiologic adaptation that conserved limited carbohydrate stores (both glucose and muscle glycogen) and made fat the predominant muscle substrate at this submaximal power level.

Phinney SD, et al. "The human metabolic response to chronic ketosis without caloric restriction: preservation of submaximal exercise capability with reduced carbohydrate oxidation". Metabolism. 1983 Aug;32(8):769-76.

Maybe put a 1/2 tbsp. ground flax seed in your eggs in the morning. The carbs would be worth it to provide you with long term energy to prevent dizziness.