As I understand it, "La La Land" is set in present day Los Angles, but makes nostalgic reference to the golden era of Hollywood in various ways alongside contemporary references. On the lot is mainly a reference to old Hollywood and old movies about old Hollywood in which being on the lot plays an important role. Is the character, Mia, trying to sneak into a closed audition, for example? I haven't seen the movie and am speculating.
The lot is short for movie studio lot and refers to the gated property of a filmmaking studio, e.g. MGM or Paramount where films were made on set vs. on location. A related phrase is backlot, the area of the studio complex where outdoor locations were recreated, e.g. a New York City street with buildings that look like the real location portrayed.
This reference to the lot with a guard at the gate who is checking what actors and personnel are allowed into the movie studio complex is from the time prior to the breakdown of the studio system, i.e. the 1960's and before. See Collins Dictionary Also, see Paramount Studio website for a contemporary description of the use of lots and back lots.
The phrase haul ass to mean move quickly seems more contemporary and less refined, so there may be a juxtaposition of phrases from different time periods.
A very useful explication of haul ass comes from Tom22 in a comment to this answer. I am now incorporating that comment into my answer. I would add that for me, haul ass most often refers to driving a vehicle. Again, I haven't seen the movie, so don't know if the character was in a car or on foot.
When you "just haul ass past" something, it implies that you are
blatantly disregarding enforcement of rules.. in this case rushing by
parking lot security. (that is clear to me without even seeing the
film from the way it is worded). You "haul ass" in a get away from a
bad situation.. a criminal seeing a police officer my haul ass.. "get
the hell out of here" comes close... but it implies you're leaving
before things get really bad. I Have 20 minutes emphasizes that he was
spotted while hauling ass and its only a matter of a short time before
the security radioed finds him. Tom22 -- see comments below for source.
I assume you understand that La La land is a phrase that means:
A notional place characterized by fantasy, self-absorption and
blissful lack of touch with reality.
See The Phrase Finder, a good online reference based in the UK.