I'd get the insurance instead from virgin mobile for 5 dollars a month.
Assuming he has it more than 4 months, that is bad advice. After 4 months, he would be paying more than the square trade warranty. Warranties are tricky, be sure to read the fine print. I am guessing you got that quote with ST by picking "other phone" (which starts it at $59) and then using some sort of coupon code. You might want to verify with them that it is still covered since it is an Android phone and they have a different (more expensive) category specifically for android phones. Also, realize it doesn't cover the battery and accidental damage (drops, spills, water damage) require a $50 deductible which kind of ruins the deal (in my opinion).
Also realize that you have a 12 month warranty from LG and the square trade one overlaps that, so you really only get a year or so. Granted, squaretrade is likely going to be easier to submit a claim to if needed than LG.
In general, most statistics show that if you don't buy extended warranties on anything, you will come out ahead (assuming you buy an average amount of things that extended warranties are sold for). You might every once in a while have something break where an extended warranty will help out, but overall the savings from not buying other warranties should compensate.
Most likely, the phone will break from dropping it or some other accident. Unless you are highly accident prone, $71 (21 for the warranty and 50 for the deductable) seems a high gamble for a phone you got for $160 (and likely can get cheaper in the future, especially after Motorola releases their android VM phone). Odds are a random circuit won't fry between years 1-2 (usually either manufacturing defects show themselves pretty quickly or the phone is good and will last for years).
All that said, if $21 makes you sleep better at night and not worry about it, then it is worth it.