It was pretty well established that Lester had trade missions, particularly for military supplies, going to the Lyrans. Pretty much a win-win for both parties . . . Lyrans get a militant and militarized destabilizing faction in the center of League space. For over 60 years they had managed to prevent the League from reforming, to the point Jessika trolls Blakists to remove them as a obstacle. The Lyrans are so unlikely to ever face the Regulans in combat- they would have to go through a LOT of League territory to reach them. And of course, for the Lyrans they can keep their mech production cranked up making money while still drinking Stone's Koolaid.
For the Regulans? They can pick up a assaults so they do not have to devote a lot of resources to trying to build that production- and typically assaults that will be beefier than what other League states build (design philosophy difference) to give them a combat edge. Not really sure what they are trading to the Lyrans but it is still economic lifeblood. Heck, they might involve in something like . . . take load of Ogres to Solaris VII & Arc Royal, sell to mercs, buy Lyran assaults and lights, come home. Someone might even be buying Ogres on Solaris VII and shipping them to Galatea when it was under the Republic to be sold at the merc hub.
To go further, the Regulans were also selling military equipment to the Cappies- namely the Tufana std & (iNARC) as mentioned in fluff. What they got from the Cappies we never really learn. Maybe the cash to buy Lyran assaults?