To go in-depth, 그러는 is the attributive adjective form (i.e. directly modifying a noun) of 그러다. 그러다 is short for 그렇게 하다, or "to do so; to do (something) that way". There are many variant forms sharing this meaning, such as 그래, 그래서, 그러고, 그러면, 그래도,and so on. 편 in 편이 means a "side" which is sometimes extended to the sense of direction or choice. Fro example, 길의 저 편에 은행이 있다, 너는 누구 편이냐?, 나는 키가 큰 편이다, 이렇게 하는 편이 낫겠다. 그러는 편이 is thus "그러는(doing that) 편(side, choice)이(subject marker)". It literally "the choice of doing that", but since the English gerund already a noun implying the choice taking, we can translate it simply as "doing that". 그러는 편이 is about the same as 그러는 것이, but 편 stresses the sense of choice more than 것.

It's hard to just give a precise translation of ""그러는", which is just "that" with an identity marker. On the other hand, "그러는 편이" is more descriptive, meaning, "(doing) that instead...". So the sentence above is, "because doing that instead is less tiring".