Should I have enought time at LHR for our connecting flight to Palermo?

I’m pretty risk averse with unprotected connections like this so I wouldn’t do it.

Long haul flights like SEA to LHR can easily be delayed 30 to 60 minutes by headwinds, air traffic control issues, minor mechanical or paper work issues. That would leave you only 60 to 90 minutes to deplane, walk into the connections area, get to other terminal,go through security screening, find your gate.

For a “connection” like this I like a minimum of 4 hours and prefer an overnight. I did something similar coming back from Sicily. I left Catania on the very first flight of the day at 6:30 got into Rome about 7:30 for a BA flight that left just before noon. I made it without any issues but it was nice to have a buffer.

Edit: I’m assuming this is on separate tickets. Miles to get to LHR and separate ticket to Palermo?

The free Heathrow express train takes about 15-20 min from T3 to T5, and there is one every 15 min.
Assuming the airplane from LAX arrives on time, 2 hours should be sufficient. If you have checked bags that is not an issue. AA and BA are partners and checked bags would be transferred. You wouldn’t see your luggage till you get to PMO anyhow.

I cannot recall many occasions when my flight hasn't been held in a stack prior to landing at Heathrow and flying transatlantic also increases the chances of delays. Personaly I wouldn't be comfortable with such a tight timeframe.

My previous comment is based on the assumption that you arrive at LHR from LAX at 12:05 on flight AA108 operated by AA. I also assumed you are flying on one ticket all the way to PMO (AA and BA are both partners of the One World alliance).
Even in the event your incoming flight is late and you miss the connection, you would be rebooked on the next available flight.
If you are flying from SEA to LHR (not Via LAX), then your AA flight is actually operated by British Airways, therefore you are landing at T5 already and all you need to do is take the people mover from the C building satellite to the A building, which takes just a few minutes.

Thanks for your promp replies. We only have miles on American (through Alaska Airlines) so can not fly British Air to LHR. The ticket from LHR to Palermo only flies a few days a week, nonstop (we would need to purchase). I'm thinking we may just fly into Milan and stay in northern Italy. We booked our flight back from Rome already (months ago). Hopefully, we can do Sicily in the future.

Becky, I don't know how long your entire vacation is, but if it's rather short, I don't think you should be at all disappointed about postponing Sicily. It has so many wonderful sights; flying there for a short visit isn't a great idea, in my view.

I made a similar connection at LHR but when returning to US( it was Madrid to LHR to US) and had 1 hr 30 min. Use the Connection tool on Heathrow’s website, very helpful and accurate.

Alaska FF miles can buy BA flights. When I was looking for my trip there were oodles of BA flights, but only a few AA flights to be had.
This for SEA toAMS. Lots of BA flights via LHR. I know you have a different destination, but SEA to LHR on BA is easy using ALaska FF Miles.(or am I misunderstanding something?)

We don't have enough miles to fly BA, thus only looking at AA. We're hoping to maximize our vacation time in Italy. We may fly into Paris, then fly into Italy later that day. As I said before, we already booked our flight home from Rome, with Alaska FF miles, so we can stop in Chicago for Passover with family March 30. We now finally have enough time to book our flights to Italy. We can go anytime after March 9. But alas, no 20,00 awards flights into Rome anywhere near then.