Another perspective, from a woman in her 70s. It's lovely that you're being so thoughtful. But this whole thread reminds me of a train journey I made a little while ago. A young man took a seat next to an older woman, maybe in her 60s. For a hundred miles or so he told her loudly about his life - university, sports, ambitions. She got off at her station, "lovely to meet you" etc. He then phoned a friend and told them, "Yes I'm on the train, just been chatting to an old dear, keeping her company..."
All of us "old dears" in the vicinity were smirking and side-eyeing each other, it was hilarious. My point is, are you sure she's decrepit? I'd be a little taken back if someone did chores for me unbidden, however well motivated. And although I live alone, I'm not lonely. I'm not criticising your kind impulses, just warning you against being a touch patronising.