I've managed to get this working now after spending a good few days playing around with the configuration.
The plugin was disabled whilst I got the rest of W3's configuration as we want it, and I decided to test Lazy Load again today - when much to my delight it worked instantly.
I've made sure jQuery is loading first and all other js loads in the footer, and it seems fine now. Sorry I can't be more constructive as to the exact details.