I bought a phosphate free detergent from Aldi (I can't remember the brand name, but it's not a known brand and it's the only one they sell), and it worked fine....just found that it actually made suds in the LG, so had to use less of it.
I used it in a giant load that I did with the machine packed full of mostly greasy/oily dishes and pots with some stuck on stuff like oatmeal stuck to the bottom of the pot, and it did a fine job. I expected maybe greasy streaks on the glasses, but there were none. I found it did a better job on the utensils on the bottom rack.