Are there any luggage lockers at York railway station?

YES! there is left luggage, but it is not lockers. Basically you hand your bag over and they store it in a large room with a bunch of other bags. It would be wise to lock your bag and to not leave anything of value in it! As i recall, it wasn't too expensive.

... from Northern Rail website ...

York Station Left Luggage

Europcar Left Luggage Office, platform 1, York Station, York YO24 1AY

Tel: 01904 656181

opening hours: mon - sat 0800 - 2030 sun 0900 - 2030