Simple response: account bind the Lobi, don't offer Lobi for free anymore.
I also have multiple toons and I'd really be much, much more open to lockboxing if I could decide where to move my Lobi after the fact. Sometimes it isn't much of an issue, but I regularly play KDF as well as Fed, and since you can potentially get different rewards dependent on faction, splitting the Lobi pool is a pain.
What would we lose? A handful of free Lobi once in a great while when we have episode replays? Big whoop. I'd rather control where the stuff that I pay for goes.
Personally i cant find any excuse for the account binding mechanic especially in a game like startrek. the federation generally supports free trade and most species engage freely in intergalactic trading. account binding should actually be removed completely as it prevents good high quality items from getting on the player market and keeps the in game market artificially inflated. just look at Eve online and how it has no binding mechanics what so ever yet maintains a relatively stable in game economy
Account bound Lobi would be great, but the freebie ones could be a problem.
22 Lobi for a single toon doesn't sound like much, and indeed most Silver would only have one extra toon, making for 44 in all across both.
But Golds have three, so 66 Lobi. Two pets or a weapon right there, if still not a truly meaningful amount.
Lifers get two more character slots via Vet Rewards. Five toons makes that total 110. That's half a set weapon/console or a low end outfit.
More extreme cases need to be considered, too. I have fourteen alts. That's 308 Lobi. Or a whole shuttle with a sliver of extra Lobi. And fourteen is definitely not a high number of alts, if rumors have any grain of truth to them.
I'm not saying I disagree with account-bound Lobi, I'm just saying dismissing the exploit presented by that idea because it's paltry with a single alt is kind of short-sighted.
So get rid of the Freebies.
Seriously, it's not a difficult work around. Drop the freebie Lobi and make those little orange carbon clusters account bound.