connecting flight from Heathrow to Milan

Since you are only transiting the airport, you will stay airside and don't need to clear either Immigration or Customs. You will need to clear security before proceeding to your connecting flight. As long as your flights are all on one ticket, your checked bags should be checked through to Milan and won't need to be picked up and rechecked at Heathrow. It's a tight connection, so make sure you already have your boarding passes for the Milan flight when you leave LAX. Perhaps ask the flight attendant about your gate number before arrival. Otherwise, look for the large departure board after deplaning.

It's a tight connection, but if BA has issued the ticket, they are responsible for getting you to Milan. You do not go thru Customs, but probably an electronic passport or boarding pass machine. You then have a security line where you put your luggage thru the x-ray.
If you leave LAX on time, you'll probably arrive a bit early. Check FlightAware for the on- time performance of the flight.
With tight connections, checked luggage often doesn't make it, so hang on to your belongings.
May be helpful to check the time of the next flight to Milan, just so you know.
Good luck!

This is on one ticket, correct? You will not go through customs or immigration, but you will go through security to get to your next gate. The “minimum connect time” within T5 is 60 minutes, so you should be fine, as long as your flight from the US is reasonably on time. If it is too late to make the connection, BA will put you on the next available flight to Milan.

Note that T5 has three separate buildings, 5A, 5B, and 5C. They are connected by an underground train. When you get off your plane from LAX, you just follow the purple “Flight Connections” signs. Do NOT go to “arrivals”. At some point there will be a choice point for going to other terminals but you follow the signs to stay in T5. They will take you to T5A, which will involve the underground train if you landed at a B or C gate. You will go through security before you enter the main departure area of T5A. There you will find the Departures board where you look for your flight and departure gate. It could be in B or C, so you should head straight there as soon as the gate is posted. The path to B and C is well-signed, as is the path to A gates.

As for checking your bag versus carry-on, it could actually slow you down to have a carryon through the security screening, as they are very strict at Heathrow. So make sure you have no liquids other than what fits in your 3-1-1 bag. Do not mistakenly bring a water bottle with water in it from the plane. And note that laptops, tablets, Kindles, iPads etc. all must come out of your luggage or backpack and be put in the provided bins.

One time my daypack got pulled aside for inspection even though I was careful to do everything right. They did not find anything wrong, and never did tell me what they thought was amiss. But it delayed us about 15 minutes.

We generally like the convenience of check-through bags when flying BA to Europe, but with that short connection time I probably would do carry on, due to the slight chance your checked bag might not make the connection. That happened to our daughter when she flew to Rome to meet us, and she was without her luggage for 3 days. Fortunately we were spending a week in Rome, so there was time for the bag to catch up with her, and BA did deliver it to our apartment. But she got pretty tired of the same clothes.

Go to this website:

Heathrow Flight Connections

Plug in your flight information and it will give instructions on what to do.

Thanks to all for this valuable and detailed information. I think we'll know what to do in any event. You put my mind at ease.
Ciao!