I had a connection at LHR about a year ago (to be clear: a single Delta ticket involving a KLM flight from AMS to LHR connecting to DL from LHR to SEA), and at the time, the official guidance was that the ETA was required. I went ahead and paid the trivial fee for the electronic travel authorization; I think it was £10 at the time (about $13 USD). Yes, my itinerary involved a change of terminal, but even if it had not, my understanding is that the ETA is required of American citizens.

FYI a change of terminal at LHR when you're traveling on the same ticket will not involve transiting any immigration or customs checkpoint; you will ride an intra-airport bus, and after exiting the bus you will clear a security checkpoint (which I don't really understand since the bus services only sterile areas, but whatever).

I highly doubt you'll miss the £10 (or perhaps £16 as the price may have gone up) and you'll have peace of mind that you're covered. And the last thing you want is an argument with a Delta counter person or gate agent. And if something did go awry with your travel plans and you needed to overnight at LHR, you'll have that scenario covered. And the thing is good for two years.