The Spain international moved to the west London side in a £58m deal from European giants Real Madrid in the 2017 summer transfer window.
Morata hit the ground running with a consolation goal and an assist in Chelsea’s 3-2 loss to Burnley in their Premier League opener at Stamford Bridge.
The 24-year-old centre-forward failed to get on the score sheet in a 2-1 win against Tottenham Hotspur on Wembley but was back amongst the goals in Chelsea’s 2-0 victory over Everton.
The Blues striker netted in successive games to help the defending Premier League champions ease to a 2-1 win against Leicester City at the King Power Stadium.
Morata has already impressed in the Premier League but Chelsea will switch their focus to the Champions League on Wednesday night for the visit of Qarabag.
Chelsea’s record goal-scorer Lampard is backing Morata to shine in Europe’s premier club competition throughout the 2017-18 season.
“Alvaro Morata has already made a good start to his Chelsea career in the Premier League but playing in the Champions League will suit him even better,” Lampard told the Evening Standard.
“I watched him from afar when he was at Real Madrid and Juventus and I think he is the complete striker. Technically Alvaro is fantastic, as is his movement. He will be in his element on this stage.
“The Champions League is the top competition in the world. I felt it when I played, your standards had to step up.
“With players of Morata’s ability, performing in the Champions League is what it’s all about. It’s imperative.”
Chelsea have won three of their opening four games in the Premier League to leave the west London side in third place in the table.
Morata was one of seven summer signings at Stamford Bridge following Chelsea’s title success last season.
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