And now that we know he's a Darkfriend, it's quite conceivable that he came to Sylvase prior to the battle for Caemlyn with the offer of killing her grandfather (which, if the hypothesis that he sexually abused her is accurate, she'd jump at) in order to ingratiate himself for a High Seat not sworn to Arymilla.

Remember that the Shadow's plans for Caemlyn involved Elayne becoming queen; they spent a great deal of effort sending people like Hanlon and Duhara to try to control her, their Black Ajah mole never tried to assassinate her, and they had more than enough spies inside the city to know that Elayne's army could defend Caemlyn against Arymilla. So on the eve of an attack, Jaq Lounalt gets into Sylvase's good graces, someone who he expects will switch to Elayne's side after the defeat, to therefore get another inside man in the Palace.

The abduction by the Black Ajah was totally unplanned for and unexpected, an emergency measure taken after Elayne showed up on their doorstep. It was uncoordinated with the efforts of other Darkfriends in the area, so Lounalt's part proceeded as planned.