Can I run this hard drive on 12Vdc 1.25A instead of 1.5?
Yes, there is a risk that you will lose data if you try this: if hard drive draws more than 1.25A and the 1.25A supply can't supply this, the voltage supplied will drop to lower than 12V. This may cause the drive to stop working suddenly in the middle of a data write, which could cause data corruption. Conceivably this voltage drop might also damage the electronics in the drive.

I think the chances of this sort of damage occurring is fairly low (probably the drive draws less than 1.25A almost all the time), but it is a risk nonetheless.