Basically Lga is closed and you aren’t allowed to enter but the reality can change depending on the weather so if there are storms and tons of cancelled/ late arriving flights the night you are trying to get in you might be able to access the airport because it will have stayed open later and have a certain number of stranded passengers on a decent weather day it will be tougher,

from what I have noticed arriving on delayed flights coming in past closing almost all doors are locked with one or two doors opened to let passengers out with security at those doors