Can Bose companion 2 speakers connect to lg 42ld520 tv?

You can connect Bose Companion 2 speakers to almost any television. For what I tried now, if your television has at least Jack output(1) or Optical output(2), you are good!

(1) If you want to use the Jack output, you need to buy a "RCA males to Jack male" cable. You plug the RCA males at the back of your speakers and the Jack male in the Jack output or your television (often a headphone input).

(2) If you to use the Optical output of your television, you need to buy a "Digital to Analog converter" (around $70 with Gefen brand). It will convert the Digital output (Optical) into a analog signal for your speakers. These converters rarely provide RCA cables(male/male) and Optical Cable(male/male). So you will have to buy them too.
It might seem an expensive solution, but it can save you if you already have good speakers and your tv doesn't provide Jack ouput.