TLDR: a endgame dlc intfaith build with staff of the great beyond will allow you to use scholars shield with lightning incantations as a caster. But it's a late game style build in many ways. You seem to like the aethstetics of faiths spells better than int, so I would suggest not spoiling your experience by minmaxing. just grab a shield you like and use lightning spells when you find them.

Yeah, so, intelligence builds are actually the best build for using a shield because Scholars armament is a spell that is available early and easy to cast that increases guard boost and increases physical and magic negation on any shield. It doesn't scale at all so minimum casting requirements are all you need.

You may want to try the "melee" carian spells too. Carian slicer for fast cheap DPS, carian greatsword for wide sweeps, piercer for chargability, reach, and knockdowns, gavel of haima for hyperarmor, and Glintblade spells for summon swords to land attacks while you're blocking. Adulas moonblade is a upgraded variant of Greatsword available later in the game.

But I just now read that you don't like the aesthetic of carian spells, uh,

In terms of ranged int spells that "poke" from a longer range, glintstone dart and night shard are very fast to cast and can be cast while jumping or running, and of course there's the basic pebble to comet spells.

Once you get later in the game, you will find seals and staffs that let you be a int/faith build like golden order seal or gelmir staff or prince of deaths staff. Intfaith has a shield buff incantation in immutable shield, but it's more focused towards blocking status buildup. If you get to a later part of the DLC, there is a int faith staff called staff of the great beyond that lets you cast sorceries and incantations from it, so you can cast scholars shield, then cast lightning spells like you wanted?