Grantham has ticket barriers, Peter, I don't know if platform tickets are available or not. There is plenty of parking, but it's very expensive at the station, £11 per day for cars, I don't know what is charged for scooters. It might work out cheaper to go to perhaps Bottesford or Ancaster, the nearest station to Grantham and park there and take the train into Grantham, the fare is £4.10 day return from either. The platform staff at Grantham are very friendly and helpful in my opinion, and the coffee and cakes in the Pumpkin cafe are excellent! (Get yourself a "Bite" card and get a 20% discount.
www.bitecard.co.uk ) Hope this is helpful and you have an enjoyable visit.
Regards, 62440.