When a horse is visibly struggling to keep up in the run, or out the back dead last, they are said to be lucky to beat the ambulance home.
In other words, it will be a miracle if they even finish the race, that's how badly they are running.
An exaggeration that simply means that a horse has no chance of coming within cooee of the winner.
"Steve is on that nag at the back. With the way he's been punting today, it'll be lucky to beat the ambulance home."