Q can't crit, and if I built Thornmail, you'd be taking most of that damage back on yourself. All I need after that is sustain+damage items and I'm out-trading you by miles.
Before you even try to say it, no. Lifesteal does not out-scale Thornmail. Thornmail out-scales Lifesteal. I've done the math multiple times, and your 42% Lifesteal is not going to heal you for more than Thornmail will deal, because TM deals damage before Armor while Lifesteal heals after Armor.
Irelia's base AD at level 18 is 115.4, Trinity's proc is worth double that (230.8), and then you've got 80+80+80+75+30 AD, pushing her total to 460.4. Because of IE, your crits will be worth 1151 damage. Your Qs will deal 831.2. All of this calculated before Armor.
Base Armor across the board ranges from 66-94, unless you're Thresh (because he doesn't get per-level Armor, just his passive's Armor for souls). Thornmail adds 100, so 166-194. Physical damage will be reduced by 62.4-66% before any other boosts to Armor. Irelia's basic attacks will deal 156-173 damage, her crits will deal 391-433, her Trinity proc will be worth 78-87, meaning her Qs will deal 282-312. Her Lifesteal gets 42% of those damage numbers; she heals 65-73 from non-crit basic attacks, 164-182 from crits, and 118-131 from her Qs.
Thornmail deals 30% of the physical damage back before Armor as magic damage. Irelia's resistance is 52.5, reducing that to 19.7% damage return. Irelia's non-crit basic attacks will return 90 damage, her crits will return 226, and her Qs will return 163.
Thornmail has entirely shut down your Lifesteal, while also halving your damage output.
And I still have 5 item slots.