I bought a LG BP125 a while back, from Noel Leemings.  They made it clear there were no region free players, except the fancy panasonic one (or something) which cost several hundred dollars.  I of course, bought this cheap model and resigned myself to never watching the dvds I bought overseas, unless I downloaded them illegally to do so.

For other LG models, there are pretty well substantiated reports that you can burn a directory (RMTM0000/SCARLET/kpjc19_1.dvd) to a cd or dvd with certain contents in a certain way, and when inserted, a menu pops up where you can select region 0 (region free).  It is not expected to work for the BP125.

However, I've been reverse engineering the latest firmware, and found the following string "/VIOLET0000/RUBICON/MontBlanc.dvd".  In the code event handling, presumably on disk insertion, it tries to open that file, and if it finds it, it opens a region menu resembling exactly what the BP320 users describe (select a region, then press pause).  I cannot try this, as my dvd unit in my laptop died a year ago, and only scars anything put into it.

Does anyone have a BP125 player, and a working dvd/cd burner, and some old blank cds which they want to try this with?  Note that the BP320 case specifies that the cd should not be joilet, and should be iso level 2.  It probably pays to read the linked thread and to choose an approach known to work.