Will we have enough time?
 

Welcome to Flyertalk, Ladylocks... I strongly recommend taking an earlier flight on Southwest. In a perfect world, under perfect conditions, that transfer from T1 to T2 would be easy. However, I think you are cutting this much too close. Try for a flight which will get you to LAX closer to noon or at the very latest, close to 1. The Security lines at LAX can be agonizingly slow,
Good luck

As I hope you know, if your Southwest flight is late or cancelled and you miss your separately ticketed Alitalia flight, Alitalia can cancel your ticket for being a no-show and you will be at their mercy to give you any compensation of future flight. Agree with obscure2K that you should give yourself a lot of time, booking an earlier flight and having the flight you are currently booked in as a possible backup plan.

Plus 2 on the above. If your next flight weren't international, it might be worth it to try but as it is, you have too much to lose. Try to find an earlier flight to LAX.

To re-iterate what was said above, give yourself more time. Here is my personal experience not LAX but SFO. We had two hours between flights, but then there was weather (fog) at SFO so the departure was set back ~30-40 minutes. Workable. We boarded then sat on the tarmac for another 30 minutes. Okay cutting it close. We land, exit the plane with ~35 minutes til departure, and run/walk from one terminal to another. The security lines is a mess. We walk right up to the front and get through. We get to the boarding with ~15 minutes to spare. BUT remember boarding closes 15 minutes before departure. So yeah we made it. Everything was booked on single ticket so we would have been safe had we missed the flight. But that is not your case and there are horror stories of people having to buy a new ticket after missing their onward flights.

Not even something that needs discussion unless you happen to be someone who wins every time you buy a lottery ticket. :)

Bad idea.

As you are on separate tickets (WN does not interline with other carriers, so not a choice if you choose to fly WN), you bear 100% of the risk of a now show on your AZ flight. In that case, AZ will cancel your ticket, both out and any onward and return segments as well. Whether you can preserve any value is purely up to AZ and unlikely at LAX. This means purchasing new tickets at walk-up fares.

Given the significant financial penalties you face, I would allow at least 3-4 hours, particularly because you must reclaim your bags from WN, drag them to AZ, check then, head through a checkpoint and off to your gate.

If I were trying something like this I would probably schedule an overnight in LA. If that SW flight were from MSP today it wouldn't have flown at all and then where would you be. But that isn't as bad as SunCountry who have apparently permanently abandoned all their passengers in Mexico today, albeit with full refunds of the tickets.