When is late too late for an I/D connection at ORD?

I am booked on a LH/UA connection to the last flight of the day to LAS with a scheduled connection time of 1:55, yet I see my incoming LH flight is late pretty reliably over the last two weeks anywhere between 20 and 45 minutes every day. Like yesterday for example it was supposed to arrive 6:15 but did not arrive at the gate until 7:11 and doors open even a little after that. With immigration and customs to complete before riding the train to Terminal 1 to re-clear security there I guess it is pretty obvious that an 8:10 departure is impossible to make already while stepping out of the plane.

But sometimes the situation is not that obvious as the delay is less, so at what time before your departure would you quit hurrying up in such a scenario? This comes from a non-resident that does not have Global Entry...

Thanks for any suggestions you may have!

Greetings - Dirk