I am probably overthinking this but hopefully people can tell me whether I'm likely to be in trouble or not.

Next Sunday I am flying LIS-LHR on TP, coming into T2, scheduled to reach the gate at 12:45pm. I am then scheduled to fly LHR-ORD on BA from T5, take-off at 3:35pm. I will only have hand baggage (no checked bags). One potential sticking point is that these flights are, naturally, on separate tickets. Assuming no significant delays, will this be enough time to transfer from T2 to T5 and make the flight. LHR-ORD will be in J, so presumably I will get fast track access (if/where that is a thing—it's been five and a half years since I last transferred at LHR).

One alternative I have is to switch LIS-LHR to BA so that I'm in T5 the whole time, but I would also lose an hour—that would land at 1:45pm.

I didn't give this much thought when booking flights a few months ago but now, a week out, I'm a little concerned because I've read a few horror stories. Thoughts/recommendations are very welcome.