Is there a day that is free of charge?

The outside viewing is free, you could see the garden and the urban lights design installation. The inside trip is chargeable. But I think it would be worth the time and money.

LACMA members, every day Youth (12 & under) and Teens (13–17) Residing in L.A. County Youth (12 & under) Residing Outside L.A. County NexGenLA members and one guest. NexGenLA is a free membership for kids under 17 years who live in L.A. County L.A. County residents, weekdays after 3 pm with valid ID Active-duty military (including National Guard and Reserve) and their families from Memorial Day through Labor Day, through the Blue Star Museums program Bank of America debit or credit card holders, first full weekend of every month  All visitors, second Tuesday of each month Professional Personal Care Attendant (PPCA) accompanying a paying visitor who requires such care. Complimentary admission for a PPCA may be requested at a LACMA Ticket Office. Members from 24 museums nationwide receive free general admission through the Reciprocal Membership Program.

Yes outside us free and they do have alot to see the museums have a fee

The outside viewing is free. I think there is a fee for indoor viewing.