The 21-year-old, who joined from Danish side Nordsjaelland last summer, had his season cut short after just four Villa appearances when he ruptured his anterior cruciate ligament in last September’s 2-1 defeat to Newcastle United.
Okore underwent surgery and subsequently missed the remainder of the 2013/14 campaign as Villa fought off relegation to secure a 15th-placed finish.
The Denmark international is set to join the team for pre-season training when Villa return from the summer break and he is eager to prove his worth after the backing Lambert gave him.
"The manager has been very supportive with me," he told the Birmingham Mail.
"He bought me, he showed great faith in me, and now I want to repay him. He bought for me a reason, he must have believed in my ability. I will prove he was right.
"It’s about getting up to speed, getting a good pre-season under my belt and then hopefully playing games.
"I am so determined to play well and impress and prove my ability to everyone – the players, the manager and the fans.
"I just want to be able to turn around to the manager and say ‘you were right to buy me.’ I want to repay his big faith.
"I want to develop here and be the best player I can be. I want to make a difference."