In both cases West-to-East and East-to-West jet lag does apply (not north and south / south and north). Basically your body and brain are completely out of sync due to the departure time and arrival time when travelling through different time zones.
I strongly suggest arriving a few days (atleast 3, some people prefer 1 week) earlier before your marathon. This will get your body adjusted to sleeping at the correct American / European times respectively.
Melatonin is known to help people with Jet Lag but I suggest not to take that if you are going to be a tested athlete. Some commissions ban the use of melatonin therefore risking you getting disqualified.
Going out in the sun will help you a great deal. Here are some other helpful suggestions:
- Drink water
- Frequently eating small meals (fruits and veggies)
- Avoid alcohol / caffeine / pre workouts
- Nap when you feel sleepy
- Comfortable clothing (some people prefer loose clothing like pyjamas)
Hope this helps,
Good luck on your race!