The 21-year-old summer signing opened his account for the club, scoring the opening goal against FC Sheriff before superbly winning a penalty in an impressive display
Lamela dazzled throughout, sweeping home the opening goal before showing a touch of class, weaving past two defenders before drawing Djibril Paye into conceding a penalty.
And Villas-Boas hailed the €30 million summer signing before shedding some light on the 21-year-old's problems settling in at Spurs.
Speaking to reporters Villas-Boas said: "We were waiting for a good performance for him and we got it today.
"We have been patient with him and he has delivered. He had no fear, took on people and created a lot. We saw some signs of what he can do for us and hopefully from now on he’ll do this for us.
"Adaptation for him has taken some time for personal reasons.
"Not speaking the language is never easy, completely opposite social life to Italy, change of city, no family here and the fact he faced tough competition with Townsend's explosion.
"All of those reasons add up and the player is on the right track."
Jermain Defoe converted the spot kick Lamela won to put Tottenham 2-0 up, also overtaking club legend Martin Chivers' European goalscoring record with his 23rd goal in continental competition.
Villas-Boas spoke highly of the striker, adding: "We were expectant and glad it happened today. We were trying to put him through on goal, Erik did well to create that chance for the penalty and he slotted it home.
"We are all particularly happy for him, it’s a great honour and will stay in time as did Martin’s [Chivers] and it will be difficult to break.
"I hope it means this club will continue to the later stages of this competition and makes it even more prestigious."
Villas-Boas also revealed that Hugo Lloris would definitely start the game against Newcastle on Sunday.