Ludans echo

This is intentional. Luden's Echo procs off of spell damage, however, when it comes to this, Ezreal's Q is treated as an auto attack, not a spell. This means that it will proc anything that procs off of auto attacks (like lifesteal and Sheen's Spellblade passive), but it will not proc effects that proc off of spell damage. This includes Luden's Echo, Rylai's Crystal Scepter, and Liandry's Torment.