Fortunately I brought my Jepps home today so I can give you an answer. What you heard was a Tower Enroute Control clearance. Here's what Jepp has to say:
Within the national airspace system it is possible for a pilot to fly IFR from one point to another without leaving approach control airspace. This is referred to as "Tower Enroute" which allows flight beneath the enroute structure.
My Jepps have 4 pages worth of routes from any of the airporst within the boundries of Socal Approach. Basically there is so much "local" approach control that a pilot on this routing will never have to contact Center to get to where he's going.
So the "Lima 16" routing is the LAXL16 route between LAX and any of the San Diego airports. The clearance follows a series of VOR radials leading to the Mission Bay VOR, then most likely a clearance to the specified airport is given.
Hope this helps!