Lizarazu was impressed with the performance of Payet for France against Switzerland in the Euro 2016 Group A game on Sunday evening.
The West Ham star did not start the match for the home team, but he came on as a substitute in the 63rd minute.
The former Marseille attacking midfielder played well after coming on, and was unlucky not to score when his brilliant volley from Moussa Sissoko's cross struck the crossbar.
During his time on the pitch, the 29-year-old took three shots, had a pass accuracy of 87%, put in one cross, and made one block.
“As soon as @dimpayet17 touches the ball, there's a thrill,” Lizarazu wrote about Payet on Twitter. “There is something happening. His confidence is impressive.”
Payet has been one of the best players at the European Championship in France so far.
The West Ham attacking midfielder has scored two goals and created 14 chances in three games for his national team.