Lorien's castle income isn't actually that low. Yes, you have only five build plots, but all your buildings generate resources. Dwarves and Rohan have seven plots, but if we assume that they build one barracks and one forge, they don't have more space for resource buildings than Lorien has. With smaller camps it's four for Lorien and six for everyone else, but again the other factions can't spend all their plots on resource buildings.
A Lorien castle at rank three with one fully upgraded Borderguard house produces 200 resources and grants 630 command points. A Dwarven castle with five mines, three of them upgraded for resource production and two for command points, produces 192 resources and grants 870 command points. In terms of resources Lorien is actually very slightly ahead, but I agree it's a discrepancy in command points. However, I don't see a fundamental issue with the border guard house granting command points. It's your basic barracks and you should have at least one anyway, and it's more vulnerable to attack than the Citadel - same as the command point structures for all other factions, which can also be destroyed. So I think the simplest step would be to just increase the command points for each border guard house by 50% (from 480 altogether to 720). That way, you get a more solid CP foundation from one guardhouse and can then choose whether you want a second in your base or upgrade one or two mallorn trees. In terms of overall production, you won't lag behind other factions in either case because they lower their production with each resource structure they dedicate to command points.
The pikeman issue might hint at a more fundamental problem though. Lorien's pikemen are not actually weaker than, say, Dwarven pikes, and Dwarves don't even have elite pikes like the palace Guard. Do other factions struggle to counter cavalry with their pikes as well? (leaving aside Gondor, who have the best pikes in the game) If not, what do you think is the difference between them and Lorien when the Lorien pikes themselves are roughly the same strength? It's important to discern whether this is a Lorien issue or a more general problem.
One thing that needs to be kept in mind though: You are in fact expected to keep your pikemen strength up with your enemy's cavalry power. If he comes at you with heavily armored elite knights or even Knights of Dol Amroth, then basic Lorien pikes might well not be enough. If they were, what would the incentive be to ever build elite pikemen or upgrade them? Lorien's master blades especially are twice as powerful as other faction's forged blades and grant a huge boost in damage, while the Palace Guard can use their formation to stop cavalry more efficiently. You should need to make use of these to stop the strongest cavalry armies. Of course if you do use them and cavalry still wins, we have a problem.
Beornings really shouldn't be Lorien's counter to cavalry by the way, simply because they shouldn't counter everything. They're already good against structures, heroes, swordsmen, pikemen (in human form) and even archers if they get to them.