Griezmann started from the bench and was introduced for only the final ten minutes as Barcelona lost 3-1 to their bitterest rivals Real Madrid in El Clasico at the Camp Nou on Saturday.
The 29-year-old France international has failed to replicate the form that convinced the Blaugrana to activate his €120m release clause from Atletico Madrid last summer.
Griezmann scored just 15 goals, including nine in La Liga, from 48 appearances across all competitions last season and he has failed to strike up an understanding with star man Lionel Messi on the pitch.
Griezmann, who is yet to score in five games this season, was also an unused substitute against Ferencvaros in the Champions League in mid-week and Lizarazu believes it is time for his compatriot to try his luck elsewhere.
"Griezmann is great. He's a very, very good player and he's fantastic for France. But he isn't at all for Barcelona. This is a real problem," Lizarazu said on Telefoot on Sunday.
"He went to Barcelona with a dream of playing with Lionel Messi, but unfortunately there is no technical relationship between the two.
"He cannot find his position, he can no longer player football with Barca. It's a crisis of confidence.
"At some point it is better to cut off your hand than your arm. Do not hesitate to leave when you cannot find your place.
"When you lose your football at this point, it is better to go. It's been eighteen months, so it's impacting his head, and the situation is really critical for him."
