Lyon returned figures of 3-215 from 47 overs and 1-29 from 5.3 overs in the First Test which ended on Tuesday as India claimed a comfortable eight-wicket win with more than two sessions to spare.
Australia have been criticised for not including left-arm slow bowler Xavier Doherty in a two-pronged spin attack for the crumbling dust bowl of a pitch the Chennai curator offered, especially as the home side picked three spinners who claimed 20 wickets and India's pace bowlers made not a single breakthrough.
Waugh said on Wednesday Australia might want to make a few changes for Saturday's Second Test of the four-match series in Hyderabad.
"Lyon, who has been so impressive and was responsible for holding the attack together back home, looks fatigued," Waugh wrote in a column in The Times of India newspaper.
"The workload and the way the Indians dominated him suggests that he needs a break.
"I would not be surprised to see him replaced by Xavier Doherty for the next game."
Waugh has encouraged skipper Michael Clarke to dwell on some of the positives of the game for Australia, including Clarke's first-innings century and pace bowler James Pattinson's five-wicket haul in India's first dig of 572.