The former Roma man notched just once in 17 appearances in an injury-hit first season with the Premier League side following his £25.7million switch.
However, he scored two goals in the friendly win against Toronto before going off at half-time and hopes to go on improving under new boss Mauricio Pochettino.
He told ESPN: "It's something I would like to do (carry his pre-season form into the upcoming campaign), but I have to continue to work.
"As the season progresses I will continue to get better.
"I felt like I was able to play a good 45 minutes. Overall I think the team did really well and I'm happy with the performance today.
"I had an unfortunate injury last season that kept me out of play for quite some time. In the same way, it's helped me emotionally and morally to get better and work harder towards this season."
Pochettino was pleased with Lamela's contribution, saying: “We expect a lot from him, he's an unbelievable player.
“He needs to show us that he deserves to play, but at the moment we are happy with his performance.”