There's not a lot to be done here in the general case.
The three options you listed are pretty much definitive. You need to push information from the GM to a player, and it's unlikely that you'll know what information needs to be pushed in advance.
You could do something crazy, like write up a comprehensive wiki of your campaign world and give the loremaster access to it. But that's unlikely to be cost-effective and will seriously limit the GM as the campaign develops.
One thing that will help is to understand that the purpose of a loremaster is to provide the table with more information than they would otherwise receive, sooner than they would normally receive it. If you're just using the Loremaster as a conduit for the bits of information you would distribute normally, you need to rethink your strategy.
Think of them like a fighter. Instead of killing goblins, they hit the world with their knowledge skills until exposition comes out.
A good example of this is the D&D Fourth Edition Monster Manual, which has various bits of information about the monsters next to knowledge roll DCs. If you have the skills, you get extra information either at the start of the fight, or when the players first learn what kind of monster they're tracking.
As to providing a voice to the character... You do it the same way you provide a voice to a fighter. The player gives them a personality and something to say when they aren't spouting lore. Embellish with player commentary when lore is delivered. The DM can then play into this by couchingdelivering the lore in terms that match the personality of the character.
Of course, some specific systems will provide little bits and pieces that help or hinder this. Games which share authorship with the players will offer the loremaster a chance to write their own backstories, for example. Think Dungeon World and its tendency to ask the player questions to add to the backstory ("where did you learn this?" being a good one).