I live in LA and go to LAX about once a month. No, I've never seen hoards of homeless people in the airport. There are a lot of homeless in LA, especially in Hollywood, Downtown, and by the beach. When it costs $500k for a 1-bedroom condo, a lot of people are going to be homeless. LA is working on it. There are no luggage lockers in LA due to fear about bombs in suitcases. Maybe ask your airline what you can do about it. As the crow flies, you are very near the bike trail that winds for over 20 miles along the beach. But... following streets it's a few miles and you will get hit by a car if you walk or run. If you can figure out the luggage issue.... and are really desperate for a run, put some clothes in a tiny backpack and Uber over to the beach. There are showers on the beach at pretty regular intervals for swimmers and surfers - outside. And then you can change in a bathroom - they are usually next to the showers. It will be a gigantic hassle but you will get some sunshine and 65-70 degree weather if you arrive during the day. Good luck.