Amp Draw On Battery Over Time & Battery Run Time
Your LED is clearly operating as a switching regulator.  The current draw is almost certainly not steady, unlike an incandescent lamp.  How do you know your current meter was reacting properly?  If you used a true RMS voltmeter to measure the voltage across a known small series resistance, and calculated RMS current thereby, how would it compare to your meter's reading?  It is highly possible that your current meter was, effectively, lying.  In which case you know nothing useful for calculating battery life.  You have to know your tools, and their strengths and weaknesses, in order to use them effectively.  Cheap meters often read PEAK values, and the less steady (and/or sinusoidal) the waveforms, the worse they lie.

You need the RMS current of your LED lamp, at its operating voltage, divided into the Ah rating of your battery in order to know your system's operating time.  Your LED wants to suck more current as the battery exhausts, in order to maintain brightness, at which point the battery is also least able to provide current.  Also, drawing a 12V battery down to 10V will seriously damage its longevity.  A lose-lose proposition if there ever was one, so don't do this!