Level 3 Pyke (QWE) - 66 Base AD
Starting Item - Relic Shield (3 Bonus AD with Passive)
Q Damage - 75+1 Physical
E Damage - 95+3 Physical
Ignite total Damage - 110 True
Level 3 Lucian - 743 Health, 34 Armor
Damage from Q = 76 × 100 / (100 + 34) = 56
Damage from E = 98 × 100 / (100 + 34) = 73
Total Damage from Pyke (with Ignite) = 239
Percentage of Health lost by Lucian = 32%
... of course 15 minutes is a pretty long time, and Pyke should at least have ult by then if not other items. So let's go to level 6, maxing E first because ratios/base damage.
Level 6 Pyke (QWE) - 72 Base AD
Early Item - Targon's Brace (8 Bonus AD with Passive)
Q (1) Damage - 75+4 Physical
E (3) Damage - 155+8 Physical
Ignite total Damage - 170 True
R (1) Threshold - 250 base + 8 from bonus AD
Level 6 Lucian - 1001 Health, 43 Armor
Damage from Q = 79 × 100 / (100 + 43) = 55
Damage from E = 163 × 100 / (100 + 43) = 113
Total Damage from Pyke (with Ignite) = 338
Outside of Execute Threshold
Percentage of Health lost by Lucian = 33%
Not really in a mood to break down every little scenario, especially when it comes down to runes, other items, other summoner spells, etc. However I will make two observations based on what little research I did.
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The stun duration for Pyke's E and the execute Threshold for Pyke's Ult scale with Lethality. With Sudden Impact and Serrated Dirk, Pyke's E will stun a champion for 1.42 seconds; with all three Lethality items and Sudden Impact, it will last 1.89 seconds.
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The gray health on his passive has a level scaling, a bonus AD scaling, and a max health cap. It also lasts until Pyke heals or dies. In other words, Pyke has the staying power of Garen, the killing power of Zed, and, as of 9.14's Your Cut buff, the money making power of Draven.