So I've had this lord in my captivity for, according to when the character directory says he was "last seen", twenty-four straight days and I've yet to get a single offer of ransom. Is there some flag for triggering an offer to come in, or at this point I'll take any other means of offloading him. He escaped once in all this time and, in my hubris, I reloaded a save because I still had hope anyone would pay me for returning him.

(I'm playing Original Mount and Blade, if that makes a difference)

It is random. Personally I never reloaded for that reason and always take the first offer even if it is bad but you should play as you like to. I have never had a lord never ransomed or escaped but some take months. Just stick them in a well defended town (or castle) of yours and forget about them.