エネルギー消費の大きい is modifying 生き方 as a relative clause. This の is a subject marker used in relative clauses, and it's interchangeable with が. See: How does the の work in 「日本人の知らない日本語」?
Imagine this "double-subject" sentence:
この生き方はエネルギー消費が大きい。
As for this way of living, energy consumption is high.
From this, you can construct the following noun phrase with a relative clause:
エネルギー消費が大きい生き方
a way of living where energy consumption is high
Which is the same as:
エネルギー消費の大きい生き方
a way of living where energy consumption is high
Note that this person is saluting to the 生き方 itself, not "you" or anyone. The given translation is not wrong as a free translation, though.
Here are some simpler examples. が and の are interchangeable.
- 背が高い人
背の高い人
a tall person (lit. a person whose height is high)
(cf. 彼は背が高い。 He is tall.)
- 鼻が長いゾウ
鼻の長いゾウ
an elephant with a long nose
- 心が美しい人
心の美しい人
a beautiful-minded person