Lyness started Saturday's win at Fleetwood after on-loan Sunderland shot-stopper Jordan Pickford was recalled by the Premier League club.
His performance earned praise from Rowett who will now give the 22-year-old a run of matches to try and establish himself as the Brewers' number one.
"He is a young boy desperate for his chance and he did fantastically well," Rowett told BBC Radio Derby.
"It was an easy game to drop and spill things but he was assured and his kicking has improved a lot."
Lyness joined Burton from Kidderminster in July 2012 and made 18 appearances in all competitions last season.
Rowett signed teenager Mats Morch from Albion's Championship neighbours Derby on a one-month loan deal last week, and the young Norwegian was on the bench at Fleetwood providing cover for Lyness.