Many religions have period or specific practice including fasting. I'm aware of the eating prescriptions of monks, but are there traditions or practices involving fasting for Lay-people?
If not in scripture, are there in culturally Buddhist countries?
In Tibetan Buddhism there is a special practice called Nyungne. Essentially it is a practice on Thousand-Armed Chenrezig who is the embodiment of loving kindness and active compassion (the active aspect is represented by his standing not sitting posture, see the picture below).
The practice is done in retreat settings usually for 2,5 - 3 days. From the day one the practitioners refrain from talking and from the day two they fast and do a number of meditation sessions per day, all focused on Chenrezig. I've been told that it should done with someone who has a direct transmission on this practice and who can give fine details about it. Overall, I know many Western practitioners who took part in such retreats so it is definitely not an old-forgotten, exotic ritual.
In general, Nyungne is a purifying practice on the level of body, speech and mind and helps to nurture compassion and loving kindness towards all the sentient beings.
As you said, the monks should not eat outside the morning hours, lay people should also not eat outside the morning hours when they are keeping the eight precepts.
I would say you should also meditate with empty stomach, a tea is fine.
I'm not aware of anything else for lay people.
Buddha has advised to be moderate in eating. This should not be taken as fasting. One of two meals a day in enough to sustain the body with allowance to take any fluids like tea, herbal drinks and water but not milk. Also you can take Chatu Madura out side morning hours.
Chatu Madura is referred in Buddhist scriptures as four delicacies. The four items to make Chatu Madura are 1.Ghee 2.Bees honey 3.Sugar cane juggery. Palmyra Jaggery too can be used 4. Sesame oil. They are taken of equal quantities and whipped well.This can be used during fasting hours of the Buddhist Monks.
