While the antiquated LP store system has many problems, the two biggest issues that I think should be the primary focus of any rework that happens for it should address are overlapping rewards between factions, and intra-faction npc corp module distribution.
With this in mind, a reworked LP store should
Offer rewards unique to the faction and NPC corp.
This can be a combination of unique Faction weapons, and NPC corp-specific modules subdivided underneath that.
A good example for how this would look would be faction weapons and ships (ex. Caldari Navy Hookbill/Caldari Navy Rocket Launcher) be available for all NPC corps under the faction, with specific modules or implants being found only in specific NPC corp LP stores, (ex. Zainou implants ONLY available at Zainou stations) allowing for the value of different NPC corp LP to raise overall, due to the increased scarcity of common faction modules.
All factions have unique modules with no faction navy overlap.
A major issue with the current distribution of faction modules is how there is a wide variety of faction modules for one type of module and few if any variants of another. This can be best seen with things like tackle modules, which find common variants among Caldari, Gallente, and even Khanid LP stores but entirely lacking inside Amarr and Ammatar LP stores.
This can be solved by leaving unique weapons, ammunition, and ships as available in every NPC corp in a specific faction, but unique specific modules being available in private companies or departments underneath that faction as previously stated; this ensures even faction-wide access to modules but more specialized equipment be bound to specific NPC corps, ensuring that they all have at least one valuable and unique item to offer for their LP.
Organize NPC-corp specific factions under the tiercide model.
Having npc corps offering unique items means an increase in the overall variety of those items, and that implies a need to reduce overlap for current and new items. Using the ‘Compact’, ‘Restrained’, ‘Enduring’, ‘Ample’, and ‘Scoped’ model for module tiercide should extend to faction modules as well, allowing for a wider variety of options to be seeded among the vast number of NPC corporations that exist. While you might have the availability of faction weapons, ammo, and ships be universal within a specific faction, offering sub-faction variations of those with particular bonuses that fall in the tiercide module categories ensures access to items unique to an NPC corp’s LP, and that it has some use to someone, even if it is niche. Faction weapon scaling could still apply in the same way, with a faction “compact” version being available to a specific npc corp that can’t be found in a Navy store (example “Imperial Armaments” npc corp producing laser crystal ammo with a lower capacitor cost than Navy, but still having navy ammo be available).
Ensure all factions have a common number of unique faction ships & weapons.
Each faction, including lesser factions such as the Thukkers and Ammatar should either have a t2 and/OR faction-specific set the following: 1 frigate, 2 cruisers, 1 battlecruiser, and 2 battleships. For independent factions such as the Khanid or Thukker that already fill that role with t2 ships, they would offer a new and unique battlecruiser and battleship from their respective LP stores, as the other necessary slots are filled with their t2 ships.
Exceptions can be made for unique sovereigns like Mordu’s Legion, Concord, Sisters of EVE, and Society of Conscious Thought because they are either multinational organizations or they do not have a specific racial backround. However, the pirate factions and other sovereigns like the Ammatar, Syndicate or ORE would see a completely new set of ships unique to their LP stores.
Introducing new faction modules to items that previously had none in their respective faction LP store (ex. “Sisters Large Remote Armor Repair Module”, “Thukker Large Remote Shield Booster”, “Ammatar Large Remote Capacitor Transmitter”) allows for faction NPC corps to offer specific modules entirely unique to that faction, that can’t be found in any of the main 4 empires.
Incorporate random or timed event sales/markups for LP stores.
Adding a function where an in-game event, either lore-related or player-related like the domination/loss of an FW warzone could offer limited-time discounts on things like tags or LP costs of items from their store. This enables the hoarding of LP outside of a rainy-day fund to be useful, with pilots dumping their NPC corp LP on sales increasing activity in an area, or leaving an area for better mission farming during a negative event for that NPC corp or faction that causes a markup in price. This further encourages player mobility across New Eden, to be less inclined to permanently congregate around specific mission-running systems and remaining static. This could also be affected by such things as trading good shortages from a plague or famine that can be alleviated by selling more of the required trade good to and from certain NPC corps, giving pilots who enjoy hauling as a profession something universally useful to do as an activity.
Add more faction structure modules.
Something that has gone completely unused since their introduction is the possibility of adding faction STATION modules for Upwell structures. A Hyasyoda research lab is only available as a reward for an epic arc mission, but wouldn’t it be more useful to have as something to buy from a Hyasyoda LP store? This also can help fill the game with evening out the deficit or abundance of NPC corp or faction might have of modules in a particular area, acting both as welcome new content and a value buffer to ensure relatively even numbers across the different factions for their LP store item totals.
I genuinely believe this is the best way forward for a comprehensive LP store and faction module redesign, as it is in-line both with CCP’s history with tiercide and player needs.