In this case, I'd send a snail mail or email saying that they were really sorry to hear about the death of their old flame's father, and hoped they were doing okay. If the OF wants to, they can continue the contact.
Showing up unannounced at the front door of someone you dated 30 years ago, and have not been in contact with, is intrusive and kind of creepy, Hollywood plots notwithstanding. Give a phone call or email first, to see if they are interested.
I managed to totally spontaneously run into an ex-boyfriend last summer, at a ferry terminal which was 5000 km from the city we dated in, 10000 km from his home country, and 10000 km in the other direction from where I live now. Turns out he's living about 50 km from where I grew up. We said hi, I introduced him to my husband, but we didn't keep in touch.