Lendl became Murray's coach earlier this month and the Scot immediately responded by winning the Brisbane International.
However, Murray has yet to win a Grand Slam, losing his three finals thus far, and Lendl - who lost his first four Grand Slam finals before going on to win eight titles - believes that there are similarities between himself and Murray.
"Obviously I see the parallels between his career and my career and I want his career to end up like mine," said the 19-time Grand Slam finalist.
Lendl went on to praise Murray for his work ethic and bravery in appointing him as his coach.
"So far he has done everything asked of him and I also admire his guts for hiring me because he had to know it would create a lot of interest and that it's not going to go unnoticed and be a quiet thing and it ups the ante a little bit.
"I see a guy who wants to win, a guy who wants to work hard. He has been a pleasure to be with and work with."
The duo are currently preparing for the Australian Open, a competition that Lendl won twice in his own career, which starts on Monday.