Lifesteal and armour vs health

I was watching a BoxBox game recently and he decided to go for thornmail over a randuins, sun fire etc. At first I assumed it was because they had a Lee Sin, Renekton and Ezreal. But it wasn't for a few minutes until he explained that he got Thornmail over the others because it works better buying armour with life steal than it is to build health. I'm just wondering why that is? He never really explained the thought process. I assume its something to do with Thornmail providing more armour than the others so enemies will do less AD damage to him allowing him to benefit with the life steal more? Never really thought of it in that way. If anyone knows could you explain why thats the case?
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