Lothander's geas is that if he doesn't serve the Iron Throne (that is, he fails to obey every single order that Marek gives him), Lothander will die. That's why he can't give you his half of the antidote, or even tell you where the other half is, UNTIL you remove his geas.

I don't know if Edwin's Dynaheir quest is timed or not, but Minsc's certainly is, and so is Coran's Wyvern quest.