League of Legends (LoL) Question: BLOODTHIRSTER and Mord's passive?

try Death's Dance too if you are looking for options other than Hextech Gunblade

No. Bloodthirster (and other sources of Lifesteal) only applies to basic attacks and abilities that work like basic attacks. Morde's passive is considered a spell, and his bonus magic damage on-hit won't be counted into his attack damage for Lifesteal calculations.

If you want Morde's passive (or on-hit damage from passive) to heal him, you'll need Hextech Gunblade instead. Ravenous Hunter and Conqueror are more accessible sources of healing.