LDO voltage regulator with passthrough
The LD33 is a code for an SMT fixed 3.3V version of the LM1117, which is a semi-LDO regulator. It won't be of any help.

If you set up an appropriate LDO regulator with 12V out it alone will do what you want. Above 12V plus a bit it will provide 12V out (and will be called upon to dissipate a lot of power perhaps), and below 12V plus the dropout voltage (down to a few volts) it will provide the input voltage less a small drop, typically.



Edit: Given a potential part number, the above paragraph can be illustrated with a figure from the datasheet: 



As you can see the output voltage tracks the input voltage (above a few volts)  with a small voltage drop of some hundred of mV that depends a bit on the loading.. until it gets to a bit over 12V at which time the regulator begins to regulate and limits the output voltage to 12V nominally. 

/Edit



There are many potential pitfalls in what you are trying to do- aside from current and heat, the situation you describe implies a vehicle electrical system which has a whole associated set of concerns. Also keep in mind that a 12V battery doesn't stay at 12V- it drops as the battery is discharged- significantly. Your LED lights will probably get dim from a relatively small drop in voltage. Also, its normal to consider some kind of low voltage cutoff so the battery is not damaged by accidentally running it flat.