You’ve provided no references to these claims people have made, and I can find no such claims on the support forum for the plugin linked to, but lets humour this theory and investigate.
The bulk of the code is here in the PHP:
http://plugins.svn.wordpress.org/lazy-load/trunk/lazy-load.php
Judging from this I’d say that you might have some increased CPU usage, but not much, certainly not enough to make that big a difference, far worse things happen in popular plugins. So CPU-wise I wouldn’t point see this as too significant
The code itself doesn’t do any file IO either, so if there are more disk writes/reads the PHP is not directly responsible.
So that leaves the JS which is unlikely.
I see no reason why a page of images would cause a servers disk to become so busy. Lets say the worst case scenario, the browser loads all the images, then it loads the lazy_load source file, and for whatever reason the images are reloaded a second time as you browse down ( the browser cache has mysteriously died for whatever reason ). I doubt that this would make the hard drive unresponsive or cause a major problem.
What’s more I see no reason anywhere in the concept of lazyloading for there to be file writes. The JS has no write access to the servers filesystem, and the PHP does no file IO.
My humble opinion is that these claims are a load of b*llocks, and the onus should be on the people making the claims to back them up with evidence. This is a highly rated plugin, with code sourced from Automattic VIP itself, I doubt it would have either accolade if the claims were true.
Also keep in mind if busy drives cause IOps to increase, this is a potentially fatal flaw in storage technology. Maxing out the transfer rate on a HD would increase the demand, maxing out the transfer further, creating even more demand, and leading to a viscious feedback loop. Meaning that if the transfer rate was maxed out, the HD would become unusable until powered down. I’m not aware of any modern storage devices that do this, be they mechanical drives, optical drives, or any of the various solid state technologies.
Also you could have installed the plugin and found the answer within a minute by loading several pages full of images