Going to be trading in Crysis 2 today and am thinking about getting a JRPG to play, however I am still a bit undecided.

I am thinking about Ar Tonelico 3 or Star Ocean 4, however I can't get a new Star Ocean 4 from anywhere.

So to my main question. Do I need to have played Ar Tonelico 1 and 2 to understand what is going on in Ar Tonelico 3?

not really, there are a few returning characters that you won't get any nastalgia factor from but it doesn't affect the plot and their involvement in the third game doesn't really reference their involvement in the previous games except for a few instances.  While the games aren't quite as separate as something like FF you can certainly play and enjoy Ar Tonelico 3 without playing the other 2.