i will be landing at lax around 8am, is there any lockers where i can leave my luggage while i go shopping? is there any malls or outlets near?
Unfortunately there are no lockers for baggage storage at LAX. One option would be getting a day rate for a room at an LAX hotel and keep your luggage there. Travelodge LAX is a good option for around $80.
Whether you can store luggage at a local shopping mall I don't know so I'll leave that for others to advise.
All the best.
Or, you can rent a vehicle and keep your luggage in the trunk (or boot depending on where you are from)
Your best bet for outlet shopping may be the Citadel Outlet center on the outskirts on the eastern side of LA.
The Citadel does provide free shuttle service from various points in LA, but not LAX.
Are your bags checked through?
There are no lockers, so you'll need to rent a car and put bags in the trunk (boot)
Here is a luggage storage company near LAX:
Malls within reasonable Lyft ride away are Westfield Culver City , 4 miles away.
Westfield Century City - 10 miles. Recently remodelled.
Del Amo Fashion Center in Torrance, 10 miles
Westside Pavilion, West LA - 9 miles.
Citadel Outlet is 22 miles away from LAX.
Feel free to look up the malls to see what stores are available.
Well there is also Manhattan Village Mall which is very close, but it is a pretty small mall, only one main anchor store, Macy's.
Honestly, getting a car will make things so much easier (and probably be less expensive).