I think Italy needs the following cards plus some changes.
Cards I would add.

Engineering School: Artillery train time -30%; Heavy Cannons and Gatling Camels train time -10%; Papal Bombard train time -35% (Italy only has one factory, so it should be -35%)

TEAM Engineering School: Artillery, Fixed Gun, Siege Elephant, Flamethrower, Ram, Mantlet, Haudenosaunee Mantlet and Papal Bombard train time -15%; Heavy Cannon, Great Bombard, Rocket, Flying Crow, and Gatling Camel train time -5%

Fulling Mills: Villagers gather food from herded animals 300% faster

Improved Grenades: Grenade troopers get +20% attack and +25% siege attack

TEAM Grenadier Guards: Musket infantry and grenade troopers get +15% hit points

Artillery Hitpoints: Grenade troopers get +30% hit points; artillery get +15% hit points
Cards with changed effect.

Merchant Republics: Trading posts can now deposit generated resources directly into the Lombards and each native trading post generates 0.20 food that is invested directly into the Lombards.; Trade routes generate 35% more resources

Guardia di Finanza: Adds coins equal to 5% of the cost of all enemy units defeated by the player directly to the Lombards for the remainder of the game.

Theaters: Upgrades the Tavern to the Theater which can train Elmetto and Li’l Bombard; Elmetto use -1 population and Li’l Bombard use -2 population (I would like all civilizations to have their own version of Theaters that would allow them to train their local mercenaries)
The engineering cards are to compensate for the lack of a factory and highlight the natural advantage of civilization, artillery.
The cards that benefit the grenadiers are designed so that the civilization focuses a little more on siege and to improve the musketeer and artillery a little.
The Fulling Mills card is to give you an alternative initial boom that favors the use of grenadiers, helps in situations where hunting is insufficient or simply favors FI.
The first two modified cards seek to somewhat solve the excessive micromanagement of the Lombards and the last card is so that Italy can train the local units that belong to it. (I also think these cards would help fans of treaty games and settle this issue)
I want to clarify that the Theaters cards should enable the local units of each civilization and give them some exclusive bonus, in this case it is a lower population cost, but other civilizations such as the Spanish and Portuguese could have other changes. For example, the Spanish Cannoneer could be trained from the barracks and get an improvement to its defense, while the Portuguese Cannoneer could have more damage and base health.