Spooky
Have a look at plate 10-2D for the LAM 3A arrival - this will help answer your question. There is a warning note that states "Do not proceed beyond LAM without ATC clearance".
Should you be given a LAM 3A arrival and arrive at LAM with no further clearance then you must take up the hold (it has happened to me once only probably because ATC forgot to call us). To proceed without clearance in accordance with plate 10-2P may likely result in a chat with no tea and biccies in the CP's office.
Plate 10-2P is for use as stated for initial approach control procedures without radar control from LAM to ILS or MLS.
In the 737 I fly the FMC database defaults to the 10-2P procedure when a LAM 3A is programmed - however you must not fly this procedure but should expect radar vectors from LAM.
Part of a good loft scenario could be to give the crew clearance for a LAM 3A and then no further clearance - might get some interesting results!
Regards
Exeng