I like to have 2 hours, then any delays or slow immigration you have plenty of time usually. We went out to Vegas/LA in Oct, we had 90 mins in Chicago, thought we were pushing it a bit, actually did it in 60 mins exactly from landing to departure gate other side of airport. Although it helps we have been thru Chicago a few times.
Too many experiences of me making tight connections but not the luggage via LHR, especially if its checked thru and there is a change of terminal.
Don't bother now on the way back just get it sent via taxi back home, going there is a bit different.
You probably have a better chance if you check in again and take the luggage yourself.
Best pack some underwear and teeshirt for the other end
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