OP has incorrect information. The MCT for ORD for I-D BA-UA is 90 minutes. That is simply the "legal" minimum at which BA will accept a passenger for a connection -- thus a single ticket -- to UA. If the passenger is traveling on separate tickets, MCT is irrelevant.

If this is on a single ticket, 2:20 is plenty of time and the passenger will be rebooked by BA if it delivers her late to ORD. If on separate tickets, I generally advise no less than 3 times the MCT as a rule of thumb because missing the UA flight will mean that the ticket (and any onwards or return segments on that ticket) will be cancelled and will retain whatever value they retain under the fare rules (generally nothing). This would mean purchasing a new ticket.

Thus, all a risk tolerance assessment.