Should Ludens Echo proc Banshee shield?

this happened to me ingame where i was against a kata and i was playing support and she threw a q at my adc when roaming and it poped my banshees and i got hooked by a thresh and i was raging so hard

No, but at the same time, if ludens didn't proc it, neither should blue smite, ghosts, BotrK, etc. Ultimately, those are more drastic than Ludens.

I'd say it should.

With that said, Banshee's is a horrible item that is in need of major buffs. Perhaps one could be that getting hit by a spell effect drastically reduces the recharge time on the shield.

Luden's procs is spell damage, and frosty ghosts from FQC are spell effect, so yes, both get blocked by the shield.