The important question is whether this will all be one ticket TLV-LHR-ORD-DAY or whether there's a separate ticket in there somewhere. Assuming all one ticket, 1:15 at LHR is doable although without a lot of room to dawdle. And if an inbound delay causes a misconnect BA will rebook to whatever the final destination on the ticket is. You're right that the 1:30 at ORD will be the bigger challenge. I would not plan either of these connection times if there's a separate ticket.
If on one ticket it depends on risk tolerance. If this is the only logical/viable BA itinerary given the various flight options available, I'd go ahead and give it a try. In the best case it works, and in the worst case of a misconnect and rebooking you'll be on the longer less convenient connection times you would have had anyway.
ETA: It looks like neither the lhr-ord nor the ord-day flights that produce these connection times are the last of the day. So I'd give it a shot on one ticket and figure there will be options for a later same-day arrival if something goes awry along the way.
Last edited by CrazyJ82; Jan 6, 2018 at 10:19 am