No use to you for TLV, but as a point of reference I tried to secure exit row seats in Y on MAN - ORD - MAN last week as a back-up for GUVs not working.
Call centre confirmed it had to be done at the airport.
At Manchester check-in they confirmed only they could do it as online check-in 'shouldn't' allow it.
At Chicago they confirmed it could only be done at check-in, but sometimes they had found people snagged them in a small window at 24 hour online check-in. Apparently they are sometimes available for a short time, before the inventory is rightly blocked off for the check-in. Apparenly it is first come first serve (at ORD at least) as long as you are able to manage the emergency exit duties (if relevant)