IMO, the last place I would leave (short term store) an RV is at an airport or other such public parking area even if you could, which I doubt at LAX.  I would call the RV a "target rich" item there.  I would recommend, having faced the same issue, to store it at a CG or perhaps a friendly dealer for few dollars.  The RV won't "stand out" at a CG in storage.  At a CG its just another rig.  You might be able, depending on occupancy, to work out a reduced rate at a less-desirable site and leave it powered up.  If this is in the winter months in the northern area, even April, one must also consider colder, freezing temperatures.  Are you going to winterize it?  If not, heat really needs to really be on to protect the lines.  Just blowing them out, IMO, is not totally effective and full weatherization, just for 10 days, is somewhat of a project to undo when you return. Naturally this situation is a "it depends" as to temperatures. Leaving it powered also means having a cold fridge when you return ready for food and living.

Thoughts for your consideration.